Of 212 consumers polled, some like only animated movies, some prefer just musicals, and some like both. if 74 people like only animated movies, and 86 like both, how many people prefer only musicals?

52 people like only musicals.

There are 212 people.  We know that the only answers were only animated movies, only musicals, or both.  We also know that 74 people like only animated movies, and 86 people like both.  To find the number that like only musicals, subtract these from the total number of people:

212-(74+86) = 212-160 = 52