Answer
See the figure below.
Work Step by Step
The electron will experience a net zero force when the attraction force from the positive charge is equal to the repulsive force from the negative charge, and both forces are in opposite directions.
This will happen only if the electron was on the right side from the negative charge or the left side from the positive charge because if it is between the two charges, the net force will be toward the left (toward the positive charge).
The positive charge is $Q_1=+4q$ while the negative charge is $Q_2=-q$. This means that the positive charge is 4 times the negative charge. Thus the electron must be away from this great force because of we put it to the left from $Q_1$ it will move forward it and the repulsive force now is very weak due to distance and charge amount.
So, from all the above, we need to put the electron to the right from the negative charge.
According to Coulomb’s Law,
$$F_{1\rightarrow e}=\dfrac{k(4q)e}{r_1^2}=\dfrac{4qe}{r_1^2}$$
and
$$F_{2\rightarrow e}=\dfrac{kqe}{r_2^2}$$
Both forces are equal and in opposite directions, So that
$$\dfrac{4qe}{r_1^2}=\dfrac{kqe}{r_2^2}$$
$$r_1^2=4r_2^2$$
Thus,
$$\boxed{r_1=2r_2}$$
This means that the distance between the electron and $Q_1$ must be twice the distance between the electron and the negative charge.
See the figure below.
