Answer
$y=-6$
Work Step by Step
$9^{2y+3}=27^{y}\qquad \color{blue}{\text{ ...recognize } 9=3^{2}, 27=3^{3}}$
$(3^{2})^{2y+3}=(3^{3})^{y}\qquad \color{blue}{\text{ ...apply } (a^{n})^{m}=a^{nm},\quad a^{1}=a}$
$3^{4y+6}=3^{3y}\qquad \color{blue}{\text{ ...equate the exponents } }$
$4y+6=3y\qquad \color{blue}{\text{ ... }/-6-3y }$
$y=-6$
