Princeton caught 42 fish this summer, which is 70% of the number of fish his friend trenton caught.

I hope you actually want to know the number of fishes caught by Trenton the friend of Princeton. Let us write down all the details that are given in the question. These details will help in answering the question.
Number of fishes caught by Princeton = 42
Let us assume the number of fishes caught by Trenton = x
Then
70x/100 = 42
7x/10 = 42
7x = 42 * 10
7x = 420
x = 420/7
  = 60
So the number of fishes caught by Trenton = 60.