The answer is 25 fish. Each man throws away a fish before he takes his third of the total. So the amount of fish in the cooler must be divisible by 3 after one fish is thrown away.

First man sees 25 fish. He throws away one fish leaving 24 fish. He then takes 8 fish (24/3) and that leaves 16 fish.

Second man sees 16 fish. He throws away one fish leaving 15 fish. He then takes 5 fish (15/3) and that leaves 10 fish.

Third man sees 10 fish. He throws away one fish leaving 9 fish. He then takes 3 fish (9/3).

If you try the other numbers smaller than 25 (22, 19, 16, 13, 10, 7, and 4) that are divisible by 3 after throwing away one fish you will see they do not solve the problem.