Answer:[tex]h^{-1}(x)=-\frac{3}{2}x+9[/tex]Step-by-step explanation:To find inverse of a function, follow the steps below:1. replace h(x) with y2. Interchange x and y3. Solve for the new y4. Replace y to [tex]h^{-1}(x)[/tex] (this is the inverse function)Step 1: y = -2/3x+6Step 2: x = -2/3y+6Step 3:[tex]x=-\frac{2}{3}y+6\\\frac{2}{3}y=-x+6\\y=\frac{-x}{\frac{2}{3}}+\frac{6}{\frac{2}{3}}\\y=-\frac{3}{2}x+9[/tex]Step 4:[tex]y=-\frac{3}{2}x+9\\h^{-1}(x)=-\frac{3}{2}x+9[/tex]This is the inverse function.