Answer
$\frac{y^2}{36}-\frac{x^2}{9}=1$
See graph.
Work Step by Step
1. Given vertices $(0,-6)$ and $(0,6)$, asymptote $y=2x$, we have a vertical transverse axis, center $(0,0)$ (midpoint of vertices), $a=6, \frac{a}{b}=2$ and $b=3, c=\sqrt {a^2+b^2}=\sqrt {36+9}=3\sqrt 5$,
2. thus the equation is $-\frac{x^2}{9}+\frac{y^2}{36}=1$ or $\frac{y^2}{36}-\frac{x^2}{9}=1$
3. See graph.
