We want to find f(f^-1(x)), for that we first need to find the inverse of the function, which is f^-1(x). This is done step-by-step below:
[tex]\begin{gathered} y\text{ = 12x+4} \\ x\text{ = 12y+4} \\ x-4=12y \\ 12y=x-4 \\ y=\frac{x-4}{12} \\ f^{-1}(x)=\frac{x-4}{12} \end{gathered}[/tex]We have to use the value of f^-1(x) as the input of f(x).
[tex]\begin{gathered} f(f^{-1}(x))\text{ = 12}\cdot\frac{(x-4)}{12}+4 \\ f(f^{-1}(x))\text{ = x-4 + 4} \\ f(f^{-1}(x))\text{ = x} \end{gathered}[/tex]