Answer
$x^{24}-9$
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, $
(x^{12}+3)(x^{12}-3)
,$ is
\begin{array}{l}\require{cancel}
x^{12}(x^{12})-3(3)
\\\\=
x^{24}-9
.\end{array}