Taking advice from comments, here is what I got. Which answer is correct?
Final Answer:
For every $x\in\mathbb{R}:x\geq 0$, we have $$ \sqrt{16x^3\left(x-2\right)^2} = \sqrt{16}\sqrt{x^3}\sqrt{\left(x-2\right)^2} $$ $$ = 4\sqrt{x^3}\big|x-2\big| = 4x^{\frac32}\big|x-2\big| $$
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For every $x\in\mathbb{R}:x\geq 0$, we have $$ \sqrt{16x^3\left(x-2\right)^2} = \sqrt{16}\sqrt{x^3}\sqrt{\left(x-2\right)^2} $$ $$ = 4\sqrt{x^3}\big|x-2\big| = 4x^{\frac32}\big|x-2\big| $$