Answer
$$\frac{{dy}}{{dx}} = - 12x\cos 2x - 6\sin 2x$$
Work Step by Step
$$\eqalign{
& y = - 6x\sin 2x \cr
& {\text{differentiate with respect to }}x \cr
& \frac{{dy}}{{dx}} = \frac{d}{{dx}}\left[ { - 6x\sin 2x} \right] \cr
& {\text{use the product rule}} \cr
& \frac{{dy}}{{dx}} = - 6x{D_x}\left( {\sin 2x} \right) + \sin 2x{D_x}\left( { - 6x} \right) \cr
& {\text{use }}{D_x}\left( {\sin ax} \right) = a\cos ax \cr
& \frac{{dy}}{{dx}} = - 6x\left( {2\cos 2x} \right) + \sin 2x\left( { - 6} \right) \cr
& {\text{multiply}} \cr
& \frac{{dy}}{{dx}} = - 12x\cos 2x - 6\sin 2x \cr} $$