Answer
$12x^2y^2+2xy-2$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the product of $2$ binomials, the given expression, $
(3xy-1)(4xy+2)
,$ simplifies to
\begin{array}{l}\require{cancel}
3xy(4xy)+3xy(2)-1(4xy)-1(2)
\\\\=
12x^2y^2+6xy-4xy-2
\\\\=
12x^2y^2+2xy-2
.\end{array}