Answer
$\displaystyle \frac{x^{2}}{16}+\frac{y^{2}}{4}=1$
Work Step by Step
Major axis horizontal: $\displaystyle \frac{(x-h)^{2}}{a^{2}}+ \displaystyle \frac{(y-k)^{2}}{b^{2}}=1$
Major and minor axes have lengths $2a$ and $2b$
$2a=8 \Rightarrow a=4$
$2b=4\Rightarrow b=2$
Center: $(h,k)=(0,0)$
$\displaystyle \frac{x^{2}}{4^{2}}+\frac{y^{2}}{2^{2}}=1$
$\displaystyle \frac{x^{2}}{16}+\frac{y^{2}}{4}=1$