It's very difficult to have zero net gravitational force because there are many things in the universe such as an imperfect vacuum (small particles), the sun, other planets, asteroids etc.
If you exclude all of them except Earth and the Moon. Try using the formula F=Gmm(earth or moon)/d^2
Gmm(moon)/d(from moon)^2=Gmm(earth)/d(from earth)^2
Equate them but you need to change d(from moon) something in terms of d(from earth).