Answer
$m^6n^2+2m^3n-48$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the product of $2$ binomials, the given expression, $
(m^3n+8)(m^3n-6)
,$ simplifies to
\begin{array}{l}\require{cancel}
m^3n(m^3n)+m^3n(-6)+8(m^3n)+8(-6)
\\\\=
m^6n^2-6m^3n+8m^3n-48
\\\\=
m^6n^2+2m^3n-48
.\end{array}