I'll try my best to describe in words what perhaps is best done in person. The example I am going to use is a Post-It note. If you have one, or even a similarly shaped piece of paper, pull it out and follow along. Fold the left third of the post it note over onto itself. You should have now have a note that has a portion of its left side hanging above the larger portion. Now take a pencile, or any instrument, and punch a hole. Open up the Post-It note and presto! you have two holes.
Barron's states that to determine the number of holes you just need to count the number of folds. From the above example this is not as simple as it seems since we folded the paper once and two holes were produced. Perhaps another way of rephrasing their principle is 'the number of folds plus 1 equals the number of holes'. Or, you can think about counting the number of planes through which the punch goes through. In our example, it went through two - the first plane was the left hand portion of the Post-It and the second was the larger portion that the left side was folded over. Here is another example: form a simple accordian shape from you Post-It and use only two folds so that when it is viewed from the side, it forms a "Z." Now punch a single hole through it. The punch goes through three planes - the top of the "Z", the diagonal middle one, and the bottom portion. All of the hole punching questions are nothing more than variants of this example.
I prefer the latter method and I used that one on the DAT. In addition I would use this method in combination with working backwards from an example - I would look at the end product and try to 'unwrap' the figure in my mind by looking at the figure next to it. Doing so I was able to see that the final figure was achieved by "punching through that side, which was formed by folding over that portion, and thus if it was to be undone holes would be seen here and here" and so on.
If you are having trouble with this portion of the PAT I would advise you to work through a couple of examples with a piece of paper and mimick the folds. Try to develop an approach to these problems with the goal of being able to crank out answers without using a paper model as a guide.
