Answer
$h^{-1}(x) = \log_7 (\frac{x}{2})$
Work Step by Step
$h(x) = 2(7)^{x}$
Let $h(x) = y$
$y = 2(7)^{x}$
Swap the variables $x$ and $y$, then solve for $y$ to find the inverse:
$x = 2(7)^{y}$
$\frac{x}{2} = (7)^{y}$
$y = \log_7 (\frac{x}{2})$
$h^{-1}(x) = \log_7 (\frac{x}{2})$