Answer
$$\frac{{{x^2}}}{{36}} + \frac{{{y^2}}}{{20}} = 1$$
Work Step by Step
$$\eqalign{
& {\text{Vertices }}\left( { \pm 6,0} \right){\text{ and foci }}\left( { \pm 4,0} \right) \cr
& {\text{The equation of the ellipse is given by: }}\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1,{\text{ with}} \cr
& {\text{Vertices }}\left( { \pm a,0} \right){\text{ and Foci }}\left( { \pm c,0} \right) \cr
& {\text{Then,}} \cr
& a = 6{\text{ and }}c = 4 \cr
& b = \sqrt {{a^2} - {c^2}} \cr
& b = \sqrt {{6^2} - {4^2}} \cr
& b = 2\sqrt 5 \cr
& \frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1\,\,\,\, \Rightarrow \,\,\,\,\,\frac{{{x^2}}}{{{{\left( 6 \right)}^2}}} + \frac{{{y^2}}}{{{{\left( {2\sqrt 5 } \right)}^2}}} = 1 \cr
& \frac{{{x^2}}}{{36}} + \frac{{{y^2}}}{{20}} = 1 \cr
& \cr
& {\text{Graph}} \cr} $$
