We know that the gravitational force is proportional to (m₁) · (m₂).
Now we want to know the force between (2·m₁) · (2·m₂).
Well, that's just the same as (2·2) · (m₁)·(m₂), which is 4 · (m₁)·(m₂) ... four times the original force.
So in this question, the new pair of gravitational forces will be 4·F in each direction.