Let's use the variable x to define the fish speed, and the variable y to define the current speed.
If the fish swims 12 miles upstream in 4 hours, the relative speed in this case is 12/4 = 3, and it is the fish speed minus the current speed, so we have:

Then, the return trip takes only 3 hours, so the relative speed is 12/3 = 4, and it's the sum of the fish and current speeds:

Adding both equations, we have:

Now, calculating y, we have:

So the rate of the current is 0.5 mph, therefore the correct option is A.