All the answer provided till now are wrong. We missed one point that minute and hour needle meet two time in 1Hr 5 Min (not in one hour). Remember if we start from 12, thxt meet of needle would be at 12:32 and next would be at 1:05.

So in 12 hours both the needle will meet at 11*2 = 22 times or in 24 Hours its 44 Times

Ans: 44