Let the net field at any point P from the earth is zero which is at distance x from the centre of the earth.
Then,the intensity of field at P due to earth =GMex2
the intensity of field at P due to moon =GMm(D−x)2
For no intensity at P.
GMex2=GMe81(D−x)2
taking root we get, x=9(D−x)
or x=9D10