Since it takes 12 hours to fill the pool, 1/12th of the pool can be filled in one hour. Since it takes 15 hours to drain the pool, 1/15th of the pool is drained in one hour.
But it drains slightly slower than it can be filled. If the drain was left open, then of the pool was filled in that three hours. Therefore, 19/20 remains to be filled.
Since the plug is now in place, 12(19/20)=11.4 hours to finish filling the pool.