Answer
$9y^2-24y+16$
Work Step by Step
Using $(a\pm b)^2=a^2\pm2ab+b^2$ or the square of a binomial, the square of the given expression, $
(3y-4)^2
,$ is
\begin{array}{l}\require{cancel}
(3y)^2-2(3y)(4)+(4)^2
\\\\=
9y^2-24y+16
.\end{array}