Answer
$(x+y)(3b+4)(3b-4)$
Work Step by Step
$9b^{2}x-16y-16x+9b^{2}y=$
Group the terms containing $b^{2}$ and factor in pairs
$=(9b^{2}x+9b^{2}y)+(-16x-16y)$
$=9b^{2}(x+y)-16(x+y)$
$=(x+y)(9b^{2}-16)$
The second parentheses hold a difference of squares $(3b)^{2}-4^{2}$
= $(x+y)(3b+4)(3b-4)$
