In a three-digit number, the hundreds digit is greater than 5, the tens digit is greater than 4 but less than 8, and the units digit is the smallest prime number. How many three-digit numbers satisfy all of these conditions?

The hundreds column can be 6,7,8,or 9. That is 4 possibilies

the tens column can be 5,6,or 7 that is 3 possibilities.

The unit column has to be 2, only one possibility

so there are 4*3*1 = 12 possible numbers