Sal, I'm surprised that your cabinet door is hollow. Usually, it's just interior doors that are. If the hole isn't more than 2 inches in any direction here's how you fix it.
Take a piece of heavy cardboard and punch 2 small holes in it so it looks like a big button. Run a piece of string through the 2 holes and tie it off near the holes. After cutting the cardboard to a size about an inch, total, bigger than the hole, fold the cardboard once so it will slip into the hole while you are holding the string.
When the cardboard is in the hole, let it unfold and pull it up to fill the opening with the string. Apply some Minwax Wood Filler, the 2 part kind, or Bondo to the hole with a putty knife. The cardboard will give it something for the filler or Bondo to stick to.
Don't worry about trying to fill it all in one try. It's better if you don't. Let the filler set up for an hour and then cut the stringclose to the filled area. Then you can apply another coat of the filler and "hide" the string ends. Sand and apply more filler if needed.
There may be a bit of a trick required for sanding. If you push down hard, the wood might flex a bit and either come unstuck or pop down into the door cavity. Sand gently but with fairly rough paper, probably 40, 50 or 80 grit until you are very close to level and use a sanding block. Then you can go to finer paper but continue to work gently and use the sanding block.
If your kid throws a fit and punches or kicks a hole in his or her door, you fix that the same way. The difference is that they get 3 strikes and with the third strike, the door comes off until they can respect it. A week or so like that makes a pretty good lesson. Ask me how I know.