Draw a pencil mark on one door at the spot where you want to attach your hook. This can be at any height, depending on whether you want younger kids to be able to reach it. Be sure to hold the hook against this spot with the doors pulled shut to ensure that it is close enough to the edge to reach the other door.
Drill a hole in this spot, then screw the eye with the hook attached into the hole. The bit you use should be the same size as the screw on the eye. To avoid drilling too far through the door, start by making a small hole and then hand-screwing the eye screw in. If it resists too much to screw in by hand, drill your hole a little deeper and repeat.
Thread the hook through the other eye. Pull the closet doors shut, then press the screw tip of the second eye into the door to mark where you need to drill. This ensures that the hook and eye line up properly.
Drill a hole in the spot you made by pressing in the screw. Insert the second eye. Thread the hook through the eye to hold the doors shut and prevent them from popping open.