A counterexample is a single example that disproves a statement. In order to disprove "If an integer is odd and is between 10 and 20, then it must be prime," you must show that there is an integer that is odd and is between 10 and 20, but is not prime.

While 9 is odd and is not prime, it is not between 10 and 20. 16 is also not prime, but it is not odd.

15 is the answer because it is odd and is between 10 and 20, but is not prime, because it is divisible by 5 and 3, in addition to being divisible by itself and 1.