Answer
The vertices are $(\pm3,0)$ and $(0,\pm2)$.
The foci are $(\pm \sqrt{5},0)$.
Work Step by Step
The equation $$
\left(\frac{x}{3}\right)^{2}+\left(\frac{y}{2}\right)^{2}=1.
$$
is an ellipse. We have $a=3$, $b=2$, so $a\gt b$, $c=\sqrt{a^2-b^2}=\sqrt{5}$ and hence:
The vertices are $(\pm3,0)$ and $(0,\pm2)$.
The foci are $(\pm \sqrt{5},0)$.
