The electric force law is "inverse square." That means
\(\displaystyle F = \frac{kq_1q_2}{r^2}\)
Twice the distance implies
\(\displaystyle \frac{1}{2^2} = \frac{1}{4}\)
the force.

Another way to do this is longer, but less reliant on "hand waving."
\(\displaystyle F_{BC} = 4~\mu N = \frac{kq^2}{(BC)^2}\)

So
\(\displaystyle kq^2 = (BC)^2 \cdot (4~\mu N)\)