Which method is best way to clear the textbox values?

I agree with John. Both versions compile to roughly the same IL, so it's just a matter of preference.

Looking at method two, you might expect it to do something like:

txtHolidayDescription.Text = string.Empty;
txtHolidayName.Text = txtHolidayDescription.Text;
txtHolidayDate.Text = txtHolidayName.Text;

But if you examine the compiled IL, you'll see that the property get accessor is never called. Instead, you simply get:

txtHolidayDescription.Text = string.Empty;
txtHolidayName.Text = string.Empty;
txtHolidayDate.Text = string.Empty;

You can demonstrate this with a simple class:

public class Foo
{
    public string Text
    {
        get { throw new InvalidOperationException("Boo!"); }
        set { }
    }
}

static class Program
{
    static void Main()
    {
        Foo x = new Foo();
        Foo y = new Foo();
        Foo z = new Foo();
        
        x.Text = y.Text = z.Text = "Hello";
        Console.WriteLine("Hooray!");
    }
}

Running that code, no exception is thrown, which demonstrates that the get accessor is not called.