Shane has won 24 baseball and soccer trophies. The number of trophies he has for each activity is a multiple of 6. He has more soccer trophies than baseball trophies. How many of each type of trophy does Shane have

So the possible numbers are multiples of 6 smaller than 24:

6

12

18

24 is not ok, since he won both kinds of trophies, so if he won 24 soccer trophies, he'd have no baseball trophies!

if he had 12 of one kind of trophies, he'd have 24-12=12 also 12 of the other trophies, and we know that he has more soccer trophies, so we reject this

so he has 6 and 18 trophies of one kind. Since he has more soccer trophies, this means that he has 18 soccer trophies and 6 baseball trophies!