After a fisherman sold 1/4 of the fish he had caught and gave away 2/3 of the remaining fish, he had 4 fish left. What was the total number of fish he had caught?

(A) 8
(B) 16
(C) 20
(D) 32
(E) 40

Let the number of fishes caught = \(x\)
Number of fishes sold = \(\frac{1}{4}x\)
Number of fishes UNsold = \(x - \frac{1}{4}x = \frac{3}{4}x\)

Gave away 2/3 of the remaining fish =\(\frac{2}{3} * \frac{3}{4}x\) = \(\frac{1}{2}x\)
After all the above he had 4 fish left.

From here 2 methods can be used -

Method 1 :
Total number of fishes = Number of fishes sold + Number of fishes given away + the 4 he had left
\(x\) = \(\frac{1}{4}x\) + \(\frac{1}{2}x\) + 4

Method 2 : (shorter method as posted by Loser94 )
The UNSOLD fishes = Number of fishes given away + the 4 he had left
\(\frac{3}{4}x\) = \(\frac{1}{2}x\) + 4

Solving either will give you \(x = 16\).