How many different 4-digit numbers can be formed using the digits 2, 4, 5, 6, and 7 such that no digits repeat and the number is divisible by four?

If the last 2 digits of a number is divisble by 4, then the number is divisble by 4
see what combos are with ending with 2 digits divisible by 4
24
64
52
72

see their combos for the first  2 numbers
24 three other numbers to pick from so 3*2*1=6
64 three other numbers to pick from so 3*2*1=6
52 three other numbers to pick from so 3*2*1=6
72 three other numbers to pick from so 3*2*1=6

6*4=24

answer is 24 ways