The problem is that you cannot use TrimStart and TrimEnd in the manner you are trying to and still get the results you need. You've almost got the Substring method correct, although you can get better results with a minor change. You don't even need to use the TrimEnd. And its a good idea to determine the length of the String using the Length method, rather than using a static number like "6". This will avoid problems when your text is less than 6 characters, as in the word "days".
You do need to remove the space from the text, but you need to use TrimStart on a separate line.
CODE
Number = CInt(DateType.Substring(0, DateType.IndexOf(" ")))
DateType = DateType.Substring(DateType.IndexOf(" "), DateType.Length - 1)
DateType = DateType.TrimStart(" ")
The reason you were having problems with as you post previous to your last post. Is that you probably never modified the date. You just display the modified date directly in the TextBox. You are going to run into the same problem here. Do you see how I modified the first IF statement?
You need to actually modify the date stored in the date2 object. Then put the value of date2 into your textbox. Now you can keep clicking your button and it will keep incrementing based on the value in your textbox. Make the same modifications to the other two IF statements.
CODE
If DateType.Equals("days") Then
date2 = date2.AddDays(Number)
txtDate2.Text = date2
End If