How far from the Earth do you have to be to be at true 0 gravity?

This is the question for reference.
earth weightless problem.jpg

OK you'd need to know the masses of the Earth and of the Moon... or at least the ratio of the masses

you've got a spacecraft on the line between the centres of mass of the earth and the moon and you need to find the position where the gravitational force on the spacecraft due to the earth is equal in size to the gravitational force on the spacecraft due to the moon - giving no net gravitational force.

to make it as simple as possible you might as well assume the spacecraft has a mass of 1kg - hopefully it's obvious the position would be the same for any mass.
so your equations for the force on the spacecraft will look like
GM_moon/r_moon^2 = GM_earth/r_earth

and G is a constant so you can cancel that on both sides