Answer
See image:
.
Work Step by Step
Divide the equation with $4$
$\displaystyle \frac{x^{2}}{2}+\frac{y^{2}}{4}=1$
$\displaystyle \frac{x^{2}}{(\sqrt{2})^{2}}+\frac{y^{2}}{2^{2}}=1$, which is of the form $\quad \displaystyle \frac{x^{2}}{b^{2}}+\frac{y^{2}}{a^{2}}=1 \quad (a\gt b)$
$\Rightarrow$ the foci are on the y-axis.
Center-to-focus distance: $\quad c=\sqrt{a^{2}-b^{2}}=\sqrt{4-2}=\sqrt{2}$
Foci: $\quad(0, \pm c)= \quad(0, \pm\sqrt{2})$
Vertices: $\quad (0, \pm a)= \quad (0, \pm 2)$
