Quadrilateral ghjk has vertices g(2, 3), h(8, 2), j(6, 8), and k(3, 6). it is transformed according to the rule t(–4, –5). what are the coordinates of g”?

The
explanation:

the transformation T(a, b) can be change the pre image to  the final image by following the rule as we explain below
if A(x, y) is a pre image, then A ' ( x', y') is its image, and x' = a+x, y' = b + y, where  because of T(a, b) transformation

in our case Quadrilateral GHJK has vertices G(2, 3), so the coordinates of G”
can be found with

T(-4, -5)  applied to  G(2, 3) ⇒ G' (-4 +2, -5+3)=G' (-2, -2)
 T(-4, -5)  applied to G' (-2, -2) ⇒ G"(-4-2, -5-2) =G"(-6, -7) 
the coordinates of G” are (-6, -7)