Ans: D
Note that the slopes of $L_1$ and $L_2$ are $\dfrac{-2}{3}$. Hence, $L_1$ and $L_2$ are parallel to each other. Therefore, the locus of a moving point $P$ which equidistant to $L_1$ and $L_2$ is a straight line parallel to $L_1$ and $L_2$.
Note that the slopes of $L_1$ and $L_2$ are $\dfrac{-2}{3}$. Hence, $L_1$ and $L_2$ are parallel to each other. Therefore, the locus of a moving point $P$ which equidistant to $L_1$ and $L_2$ is a straight line parallel to $L_1$ and $L_2$.
