Let the initial conditions be,
Mass of the first object = M
Mass of the second object = m
Distance between two objects = d
Force between two objects = F
By newtons law of gravitation ,
\(F_i=\frac{GMm}{d^2}\) --------- (1)
Now according to final condition, distance has been doubled i.e., distance = 2d
So, \(F_f=\frac{GMm}{{(2d)}^2}\)
Or, \(F_f=\frac{GMm}{4d^2}\)
Or, \(F_f=\frac14\frac{GMm}{d^2}\)
∴ \(F_f=\frac14F_i\) -------- (using equation 1)
Hence final force of attraction reduces by four times if the distance between them is increased by two times keeping the masses constant.