It depends on the size and build of the 12 year old. My son just turned 13, but he is pretty small for his age (5' tall and 85 lbs), and I have him set up with a Beretta 390 Super Skeet with a #60 cast off spacer and a 13.5" LOP.
Some folks will tell you to hold the shotgun with your finger on the trigger; where the buttplate falls at the crook of the elbow is then determined to be the proper length of pull. That is a load of crap. Proper LOP is determined through either using a "try" gun with an adjustable stock and then building a stock to fit (works better with adults), or having the shooter try different stocks to see which "feels" best, and which hit approximately where the shooter looks. You don't want a youngster straining to mount a stock that is too long, or having to scrunch down on one that is too short. Keeping the thumb 2 - 3 inches from the nose while mounted is probably a good starting place.
I suggest that you start with a gun that the 12 year old thinks "feels right" and go from there. The stock may require adjustments besides just LOP, such as cast and pitch, to adjust the POA to where the shooter looks. Drop me an IM message if you would like a in-depth description of this fitting process; it's easier to do than to write, but its worth the time in getting a shotgun that shoots where you look.
Good luck,
Bud