Answer
See below
Work Step by Step
The foci and vertices lie on the x-axis equidistant from the origin, so the transverse axis is vertical and the center is the origin. The foci are each 4 units from the center, so $c =4$. The vertices are each 2 units from the center, so $a=2 $.
Find $b^2=c^2-a^2=4^2-2^2=12$
$b=\sqrt 12$
Because the transverse axis is vertical, the standard form of the equation is as follows:
$$\frac{y^2}{4}-\frac{x^2}{12}=1$$