Answer
$\dfrac{4}{y^{4}}$
Work Step by Step
Using the laws of exponents, the given expression, $
\left( \dfrac{y^2}{2} \right)^{-2}
$, is equivalent to
\begin{array}{l}\require{cancel}
\left( \dfrac{2}{y^2} \right)^{2}
\\\\=
\dfrac{2^2}{y^{2(2)}}
\\\\=
\dfrac{4}{y^{4}}
.\end{array}