Answer
$x^2y^2-4xy+4$
Work Step by Step
Using the square of a binomial, $(a+b)^2=a^2+2(a)(b)+b^2$, the given expression is equivalent to
\begin{align*}
&
[(xy+4)-6]^2
\\\\&=
(xy+4)^2+2(xy+4)(-6)+(-6)^2
\\\\&=
(xy+4)^2-12(xy+4)+36
\\\\&=
(xy)^2+2(xy)(4)+(4)^2-12(xy+4)+36
\\\\&=
x^2y^2+8xy+16-12xy-48+36
\\\\&=
x^2y^2+(8xy-12xy)+(16-48+36)
\\\\&=
x^2y^2-4xy+4
.\end{align*}
