Answer
$\left(\dfrac{1}{3}-2z\right)\left(\dfrac{1}{3}+2z\right)$
Work Step by Step
Using $a^2-b^2=(a+b)(a-b)$ or the factoring of the difference of two squares, then,
\begin{align*}
\dfrac{1}{9}-4z^2
\Rightarrow
\left(\dfrac{1}{3}-2z\right)\left(\dfrac{1}{3}+2z\right)
.\end{align*}