Answer
$\displaystyle \frac{x^{2}}{36}+\frac{y^{2}}{32}=1$
Work Step by Step
With the given information,
the foci are $c=2$ units right and $2$ units left of (0,0)
the major axis is horizontal, $a=6$
so the standard form the equation is
$\displaystyle \frac{(x-h)^{2}}{a^{2}}+ \displaystyle \frac{(y-k)^{2}}{b^{2}}=1$
$(h,k)=(0,0)$
$a=6$
$c=2$
From $b^{2}=a^{2}-c^{2}$
$b^{2}=36-4=32$
so the equation is
$\displaystyle \frac{x^{2}}{36}+\frac{y^{2}}{32}=1$