Answer
$m^6-16$
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, $
(m^3+4)(m^3-4)
,$ is
\begin{array}{l}\require{cancel}
m^3(m^3)-4(4)
\\\\=
m^6-16
.\end{array}