The equation to calculate the force between two parallel conductors is:
F / l = μ I1 I2 / 2πr or by rearrangement F = l μ I1 I2 / 2πr = 3f
F/ l is the force per unit length between two parallel conductors, I1 and I2 are the currents through each wire, μ and π are constants and r is the distance between the two conductors.
Since we’ve doubled the current in one wire, reduced the other to a third, and halved the distance between the conductors, we calculate the value of the new force thus:
F(new) = (l μ I1x2 I2/3) / (2πr/2)
= 3f x2 ÷3 / (1/2)
= 4f
Note: I changed the variable ’F’, in the value 3F of the question and 4F of the answer, to small caps, to avoid confusion with large cap F which is used as the abbreviation for ‘force’.