When x pounds of force is applied to one end of a lever that is L feet long, the resulting force y on the other end is determined by the distance between the fulcrum (the lever's pivot) and the end of the lever on which the x pounds
of force is exerted,

The question is worded poorly, but it looks like you have a lever in equilibrium, with a force x at a distance d from the fulcrum, and a force y at a distance L - d from the fulcrum. You already have the equilibrium formula for this situation:

xd = y(L - d)

If you know x, y, and d, you can solve for the length L.