Every hour, the tank would fill 1/4 of the way, but it would be set back by 1/6 of it's original progress due to the emptying. So how much progress did it actually make in that hour? 1/4 - 1/6 = 0.08333333. It filled 0.0833...%
This would mean '1' = 100%, so we have the equation 0.0833... x ? = 1
Well, 0.083333 is equal to the fraction 1/12. Also, 0.083333 x 12 equals 1. You can take either of those two routes to find your answer, but we can tell either way that it takes 12 hours.
In 1 hour if the tap filling the tank runs on its own it will fill 1/4 of the tank. But if the tap that empties the tank is run at the same time it empties 1/6 of the tank. So the net result in 1 hour is that 1/4 - 1/6 = 1/12 of the tank is filled.
In the next hour the same thing happens - another 1/12 is filled.
