In fact, this kind of problem can be solved without equations.

Setting: faucet A and faucet B are turned on for x hours at the same time, which can fill 2/3.

Because a fills 1/4 every hour and b fills 1/6 every hour,

So the equation is (1/4+ 1/6)X=2/3.

X, that is, 2/3 full, both parties need to open it for 8/5 hours at the same time.