Why can't I use ratios?
There's a crucial distinction between rates and ratios, and the information given in this question is in terms of rates: 7 pumps in/per 6 hours, not something like 7 males to 6 females in a class.
If you attempt to solve it by using ratios, you'll get an answer of x = 3.42857.... If you take a quick step back and look at this logically (which you should do for all problems once you've arrived at an answer!), that means it took 7 pumps 6 hours to empty the pool, but 4 pumps about 3 hours. How would it be possible for 4 pumps to empty the same pool in LESS time than it takes 7 pumps? That seems pretty illogical, right? Also, it's not listed as an answer choice, so that's another sign that you should try a different method.