Answer
$f^{-1}(x) = \frac{x-12}{2}$
Work Step by Step
$f(x) = 2x+ 12$
Let $f(x) = y$
$y = 2x + 12$
Swap the $x$ and $y$ variable to find the inverse:
$x = 2y + 12$
$x - 12 = 2y$
$y = \frac{x-12}{2}$
$f^{-1}(x) = \frac{x-12}{2}$