Answer
The net electric field at $x = 2.0~mm$ is in the negative direction of the x axis.
Work Step by Step
In part (a), we found that the $-4q_1$ charge should be placed at the position $x = 6.0~mm$
If a $+4q_1$ charge is placed at that location, the electric field at $x = 2.0~mm$ due to this charge is in the negative direction of the x axis.
The electric field at $x = 2.0~mm$ due to the $-q_1$ charge at the origin is in the negative direction of the x axis.
Therefore, the net electric field at $x = 2.0~mm$ is in the negative direction of the x axis.
