An ellipse passing through $\left(4\sqrt{2},2\sqrt{6}\right)$ has foci at (-4, 0) and (4, 0), then its eccentricity is

y- co-ordinate of foci = 0
So major axis  is x - axis
$ae=4\to \left(1\right)$                                
Equation of ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

$\frac{{\left(4\sqrt{2}\right)}^2}{a^2}+\frac{{\left(2\sqrt{6}\right)}^2}{a^2-16}=1$

$a^2=64\Rightarrow a=8$

Now ae = 4

$\Rightarrow$$e=\frac{1}{2}$