Answer
$y^4-4$
Work Step by Step
Using $(a+b)(a-b)=a^2-b^2$ or the special product of the sum and difference of like terms, the product of the given expression, $
(y^2+2)(y^2-2)
,$ is
\begin{array}{l}\require{cancel}
y^2(y^2)-2(2)
\\\\=
y^4-4
.\end{array}