whne A*B*C*D=120=2*2*2*3*5, we can have 2,3,4,5 four different number, otherwise we may have 2,2,6,5 ,2,2,3,10, or 1,5,6,8 and so on. we can not decide whether there will be two same numbers.
when A+B+C+D=15, the four number must be 2,2,6,5 , so find out there must be nubmers which are the same
The question says "die", that means only 1-6 could be shown for each number/die. So (2,2,3,10, or 1,5,6,8 ) would not be possible For (1), 2,2,6,5 ;1,3, 6,5;1,4,4,6.... could be possible. For (2), 2,3,4,5 and 2,2,6,5 are the only two keys.