Answer
$x^2y^2-4xy+4$
Work Step by Step
Using $(a+b)^2=a^2+2ab+b^2$ or the Square of a Binomial, the expression, $
[(xy+4)-6]^2
$, is equivalent to
\begin{array}{l}
(xy+4)^2+2(xy+4)(-6)+(-6)^2
\\\\=
(xy)^2+2(xy)(4)+(4)^2+2(xy+4)(-6)+(-6)^2
\\\\=
x^2y^2+8xy+16-12xy-48+36
\\\\=
x^2y^2+(8xy-12xy)+(16-48+36)
\\\\=
x^2y^2-4xy+4
.\end{array}
