The distance between two focii of ellipse is $2ae$ . Also , $c^{2}=\sqrt{a^{2}-b^{2}}$ where $c$ denotes the distance between the focus and the origin.
Given, $2b=8$ $\Rightarrow$ $b=4$
$\therefore$ $2ae=6$ or $ae=3$ $c=3$
So, $3=\sqrt{a^{2}-16}$ $\Rightarrow$ $a=5$
So, $ae=3$ $\Rightarrow$ $e=\frac{3}{5}$
Option C is the answer.