Answer
$h$
Work Step by Step
We can see that $g$ is the leg of one of the smaller triangles formed by the altitude of the large triangle, and $e$ is the other leg of that same triangle. Additionally, $e$ is the leg of the other triangle formed by the altitude of the large triangle. What we want is the other leg of the other triangle, which is represented by $h$.
The proportion should read:
$\frac{g}{e} = \frac{e}{h}$