Answer
$A$
Work Step by Step
The point $(-2,\frac{7\pi}{6})$ is obtained by rotating $\frac{7\pi}{6}=210^{\circ}$ counterclockwise to give an angle of $+\frac{7\pi}{6}$ and then moving $2$ units backwards (opposite direction as the terminal side) on this line to the point $A$ shown.