Answer
$$\text{F}$$
Work Step by Step
The two terms have $6$ as a common factor. Factor out $6$ to obtain:
\begin{align*}
&=6(x^2-36)\\
&=6(x^2-6^2)
\end{align*}
Recall:
$a^2-b^2=(a-b)(a+b)$
Thus, with $a=x$ and $b=6$, the expression $x^2-6^2$ can be factored as $(x-6)(x+6)$.
Hence,
$$6(x^2-6^2)=6(x-6)(x+6)$$
Therefore, the answer is Option $\text{F}$.