A counterexample would be 4. 4 is divisible by 4 but 4 is not divisible by 8. 12 is divisible by 4 but 12 is not divisible by 8. 20 is divisible by 4 but 20 is not divisible by 8.
I think the answer would be 56. Bc the first job has 8 different people who could get the job and then once someone is chosen for that slot the next teaching position only has 7 candidates. So you would take 8*7 which equals 56.