$$a\left(4a^{2}-c^{2}\right)$$
Consider $4a^{2}-c^{2}$. Rewrite $4a^{2}-c^{2}$ as $\left(2a\right)^{2}-c^{2}$. The difference of squares can be factored using the rule: $p^{2}-q^{2}=\left(p-q\right)\left(p+q\right)$.$$\left(2a-c\right)\left(2a+c\right)$$
Rewrite the complete factored expression.$$a\left(2a-c\right)\left(2a+c\right)$$