If this is VB.Net and you are using a Textbox - you don't need to split anything yourself. You can just access the .Lines property. You'll get back an array of strings
You certainly can loop through the rows, like others have shown; but another approach is to use LINQ to do that work for you.
txtBox1.Lines = (From curLine In txtBox1.Lines _
Where Array.IndexOf(txtBox1.Lines, curLine) Mod 4 = 3).ToArray
What you are saying here is that you want the Lines in the textbox to be equal to all of the lines that are already in the text box - as long as the index of that particular line, divided by 4 has a remainder of three.
That sounds complicated when you type it out like that, but really, all it's going to do is give you every fourth line, and set that back into the textbox.