Explanation:
To solve \(4 \sin 4x\), let's use the double angle identity:

We know:
\[
\sin 2\theta = 2 \sin \theta \cos \theta
\]

To express \( \sin 4x \) in terms of \( \sin 2x \) and \( \cos 2x \), use:
\[
\sin 4x = 2 \sin 2x \cos 2x
\]

So:
\[
4 \sin 4x = 4 \times 2 \sin 2x \cos 2x = 8 \sin 2x \cos 2x
\]

Thus, the correct answer is:

D. \(8 \sin 2x \cos 2x\)