GIVEN
[tex]g(x) = 15 - 4x \\ h(x) = \frac{3}{2} x + 8[/tex]
NOW WE PLUG IN h(x) for x in g(x)
[tex]g(x) = 15 - 4x \\ g(h(x)) = 15 - 4(h(x)) \\ g(h(x)) = 15 - 4( \frac{3}{2} x + 8)[/tex]
NOW WE SOLVE
[tex]g(h(x)) = 15 - 4( \frac{3}{2} x + 8) \\ g(h(x)) = 15 - 6x - 32 \\ g(h(x)) = - 17 - 6x \\ g(h(x)) = - (6x + 17)[/tex]
ANSWER
[tex]g(h(x)) = - (6x + 17) \\ [/tex]
I believe you added 15 to 8 instead of using the distributive property and did not divide by 2
