I believe your problem lies in making up or deciding a variable to use in the equation of the conservation of energy.
The variable is indeed tthe height, because that is the unkown. Now, how would you use the conservation of energy?
The total energy at a point is mgl, where l is the maximum height the projectile can reach. We are assuming a value of l.
[mgl - mgh]/[mgh] = 3/4
From here, you can find the value of l in terms of h. And use a simiar equation, substitute the value of l, the height is the unkown. Solve for that unknown.