To check if a number is divisible by 4, I only need to look at the last two digits. If the last two digits form a multiple of 4, then the whole number is a multiple of 4. So I want to find the largest digit that makes the number in the circle and 2 a multiple of 4. The multiples of 4 that end with 2 are 12, 32, 52, 72, and 92. The largest digit among these is 9, so that's my answer. 
What is the greatest digit that can be placed in the circle so that the six-digit number is divisible by 4? $$3\:5\:2\:9 \bigcirc 2$$