Answer
The required solution is $\frac{1}{2}\left[ \cos 4x-\cos 12x \right]$.
Work Step by Step
One of the product-to-sum formulas is $\sin \alpha sin\beta =\frac{1}{2}\left[ \cos \left( \alpha -\beta \right)-\cos \left( \alpha +\beta \right) \right]$. So, in this question, according to the above-mentioned formula, the value of $\alpha $ is $8x$ and the value of $\beta $ is $4x$.
Thus, the expression can be evaluated as provided below.
$\begin{align}
& \sin 8xsin4x=\frac{1}{2}\left[ \cos \left( 8x-4x \right)-\cos \left( 8x+4x \right) \right] \\
& =\frac{1}{2}\left[ \cos 4x-\cos 12x \right]
\end{align}$
