How many ways to make a match if there are 4 guards, 4 forwards, and 2 centers in a gym? We know that one team is made of 2 guards, 2 forwards, and a center. There are 4 guards, 4 forwards, and 2 centers in the gym. How many different matches can they play if everyone plays their own position?
My answer is 4 choose 2 times 4 choose 2 times two choose 1 to equal $72$. Out of 4 guards and forwards, you pick two, and the other two are chosen. Same logic goes for center. Is my answer correct?
Your answer, ${4\choose2}{4\choose2}{2\choose1}=72$, would be correct if you were designating one team as the home team and the other as the visitors. But it would be the same two teams playing.  In other words, you are counting each match twice.

A correct way to count the number of matches is to realize that the two centers must be on opposite teams, so you can think of one center picking his or her teammates, which can be done in ${4\choose2}{4\choose2}=36$ ways.
Yes it's correct.
In the question, choosing the members of one team automatically determines the members of the other team.
4C2 * 4C2 * 2C1 = 72 is the right answer.