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How to change the date time format into other date time format?

I saw a lot of change date time format, but all change the string to date time and change date time into the string format.
My problem is I failed to convert the date time format (5/1/2020 12:00:00 AM) into date time format (2020/05/01 00:00:00) not string.
My value and text for date time that I saw in Watch
dueDatePicker.Value = {5/1/2020 12:00:00 AM} type is system.DateTime
dueDatePicker.Text = "Friday, May 01, 2020" type is string
and I tried a lot of methods and I also confuse now. My last method is
DateTime calibrateDate = DateTime.ParseExact(Convert.ToString(dueDatePicker.Value), "yyyy-MM-dd HH:mm", null);
And I get an error:
System.FormatException: 'String was not recognized as a valid DateTime.'
I need your help to convert the value into date time format (yyyy-MM-dd HH:mm:ss)

You don't need to convert a date to a string just to parse it back into a date. Just grab the date directly:
DateTime calibrateDate = dueDatePicker.Value;
If you want to display that date as a string, then convert it using ToString:
string calibrateDateAsString = calibrateDate.ToString("yyyy-MM-dd HH:mm");

What you are doing is how you convert a string to date, but you already have a date type, why are you converting it back to a string and then formatting the string to a date again?
You can just simply do this:
dueDatePicker.Value.ToString("yyyy-MM-dd HH:mm")

String was not recognized as a valid DateTime from DateTimePicker

I get his error at hnddate(hidden field value coming from date time picker):
String was not recognized as a valid DateTime.when converting a string to datetime parse the string to take the date before putting each variable
DateTime weekStartDate = GetFirstDayOfWeek(Convert.ToDateTime(hdndate.Value))
.AddDays(0);
DateTime weekEndDate = weekStartDate.AddDays(14);
the query gets the startdate by comparing to a column in datatabse which is in 2014/04/28 and the datepicker (hnddate) has 28/04/2014 format.

Assuming hdndate.Value is actually a string and its value is "28/04/2014":
Replace this:
Convert.ToDateTime(hdndate.Value)
With this:
DateTime.ParseExact(hdndate.Value, "dd/MM/yyyy", CultureInfo.InvariantCulture);
DateTime.ParseExact allows you to specify the exact format of your input string, so that it can correctly generate a DateTime from it. In this case, your format is dd/MM/yyyy.

How to get textbox date formatted as a string?

I am using a textbox with text mode set as date. What I need is to arrange the date format to MM/dd/yyyy. I know if I use DateTime.Now, it gets today's date, but I cannot get the value of user's picked date if I do like this as there is error:
string dateOfBirth = DateTime.ToString("MM/dd/yyyy");
This is how I do:
string tmpDateOfBirth = tb_date.Text;
//This below line returns todays date and not the date that the user pick on the calendar.
string dateOfBirth = DateTime.Now.ToString("MM/dd/yyyy");

You are using today's date and formatting it... You need to format what has been entered in your textbox.
string dateOfBirth = tb_date.Text.ToString("MM/dd/yyyy");
EDIT : if you are getting 'best overloaded match error'
string dateOfBirth = Convert.ToDateTime(tb_date.Text).ToString("MM/dd/yyyy", CultureInfo.InvariantCulture);

Okay, here i assume your TextBox1.Text contain valid date value. So below code might help you.
string dateOfBirth = Convert.ToDateTime(TextBox1.Text).ToString("MM/dd/yyyy",
System.Globalization.DateTimeFormatInfo.InvariantInfo);

You can directly get the selected value of DateTimePicker.
Try this:
string datetime = DateTimePicker1.Value.ToString("DateTimeFormat");
See this link http://msdn.microsoft.com/en-us/library/system.windows.forms.datetimepicker.value%28v=vs.110%29.aspx

How is the user picking the date?
If you have a DateTimePicker object, you can just type
string dateOfBirth = MyDateTimePicker.Value.ToString("MM/dd/yyyy");
EDIT
Textboxes are not meant to hold datetime objects. If you need to do so, you'll have to parse its text:
DateTime dt = DateTime.ParseExact("TextBox1.Text", "MM/dd/yyyy",
CultureInfo.InvariantCulture);

Calendar Extender date picking and converting into correct format

i am picking the value from calender extender in textbox and i am getting the value in the format {"MM/dd/yyyy"} but i want it in the format {"dd/MM/yyyy"} in another textbox
( txt_actualrightformat.Text) as code shown below
DateTime wrongformat = DateTime.Parse(TextBox4.Text);
String rightformat = String.Format("{0:dd/MM/yyyy}", wrongformat.Date);
txt_actualrightformat.Text = rightformat.ToString();

DateTime is irespective of the format, format is only for displaying purpose. If you are not getting the right date in wrongformat then you can use DateTime.ParseExact with the format. and then simply
txt_actualrightformat.Text = wrongformat.ToString("dd/MM/yyyy");
EDIT:
use DateTime.ParseExcat like:
DateTime dt = DateTime.ParseExact(TextBox4.Text, "MM/dd/yyyy", CultureInfo.InvariantCulture);
txt_actualrightformat = dt.ToString("dd/MM/yyyy");

try these
DateTime wrongformat = DateTime.Parse(TextBox4.Text);
txt_actualrightformat.Text =wrongformat.ToString("dd'/'MM'/'yyyy");
or
txt_actualrightformat.Text =String.Format(CultureInfo.InvariantCulture, "{0:dd/MM/yyyy}", _wrongformat )
update:
i think the date in the TextBox4is really in the wrongformat :-)
Note that "22/3/2013" It matches the format "d/M/yyyy" and doesn't match the format "dd/MM/yyyy". - for "dd/MM/yyyy" it should be "22/03/2013".
DateTime dt;
if(DateTime.TryParseExact(TextBox4.Text, "dd/MM/yyyy", CultureInfo.InvariantCulture,
DateTimeStyles.None, out td))
{
// Valid date used in `TextBox4` (NOTE : dd/MM/yyyy)!, you can use dt now as i explained above!.:-)
}

Before parsing or converting any datetime value check your calendar's date format. on your aspx page go to the calendarExtender and go to its properties then find format and set the format to dd/MM/yyyy and todays date format also do the same. Then from your code behind declare a variable in datetime type and simply pass the text box value which calendarExtender puts the date on and convert the textbox value in date time. The code will be like
public DateTime date{get;set;}
date = Convert.ToDateTime(txtDate.Text.ToString());
In sql server the value will save like "2016-02-09 00:00:00.000" this format

Trouble bringing in a string with d-MMM-yy format parse.exact to date but keeping date format and date type for sorting

As the title said I am bringing in a date string from a datatable with the format of "d-MMM-yy" or 27-AUG-06.
I need to convert it to a date type for sorting, but I need to keep the same format for display.
NOTE: I am using C#, .Net 2.0, and I am retyping this code so bear with me on typos
System.Globalization.DateTimeFormatInfo dtfi;
dtfi = new System.Globalization.DateTimeFormatInfo();
dtfi.ShortDatePattern = "d-MMM-yy";
dtfi.DateSeperator = "-";
//this is in a for loop with rowCnt being the row index/counter: loop and datatable is working fine.
//"newRow" represents a DataRow in the new table.
// the table [row] [column] is bringing in the string date like "27-AUG-06"
//colXDate IS RECORDED AS {8/27/2006 12:00:00 AM}
DateTime colXDate = DateTime.ParseExact(inputDataTable.Rows[rowCnt]["colX"].ToString(), "d-MMM-yy", System.Globalization.CultureInfo.InvariantCulture);
//#### THIS NEXT LINE IS WHERE IT GIVES ME AN ERROR "String was not recognized as valid datetime."
newRow["colX"] = Convert.ToDateTime(colXDate.ToString(), dtfi);

Since you already have colXDate as a DateTime, you don't need to convert it to a string and then back into a datetime.
Instead, try this:
newRow["colX"] = colXDate.ToString("d-MMM-yy");

Your line fails because ToString() will output the date in the format defined in the current culture and you are trying to convert it back to a date using your custom date format.
You need to set it to colXDate.ToString("d-MMM-yy").

SCENARIO: I am passing a datatable back as a DataGrids datasource. I am passing in a string field that is a date. I want to convert it to a date so that I can sort by it but I also want to maintain the same format that it was on the string that came in.
ISSUE: From some of my research it seems that the DateTime type is exactly that a datatype in whatever datatable that you put it in and is not formatable. So even though I bring in an unormal string date and convert it to a datetime via the DateTime.ParseExact, when I put it into my datetime field and try to format it (newRow["colX"] = colXDate.ToString("d-MMM-yy"); //as Scott had above) it still goes in as a set datetime format with hours...etc.
SOLUTION: So I resolved this by smoke and mirrors. I put 2 columns in the datatable, the first being the string format display date and the second the datetime type. On ItemDataBound I hid the datetime column (e.Item.Cells[5].Visible = false;) and then on the sort event I test for string date column (e.SortExpression == "colX") and if it is true I sort by the hidden datetime column.