This is a quick solve -- it reduces to finding the last 2 digits of 18²⁰¹⁸, and the last 2 digits of powers of 18 start with 18¹=18, and then go into a pattern of 24, 32, 76, 68, 24, 32, etc.

The cycle length is 4, the last 2 digits of 18² is 24, and 2016 is evenly divisible by 4, therefore the answer is 24.