If the gcf is 12 and lcm is 24, and yes I do not have a typo, what are the two numbers?

NOT POSSIBLE!

for GCM you have two numbers p*12 and q*12 p not = q p and q prime numbers

for LCM you have two numbers p*24 and q*24 what is p*2*12 and q*2*12

for example to understand:

p=3 q=7

36 84 GCF = 12
LCM not 24

now p=2 q=4 q not prime

24 48 GCF=24
LCM same 24