Consider the standard equation of the ellipse 

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$,

The distance between it's foci is $6$, so, $2c=6 \Rightarrow c=3$

and given length of minor axis is $8$ units,

hence, $2b=8 \Rightarrow b=4$

So, the value of $a=\sqrt{b^2+c^2}=\sqrt{4^2+3^2}=5$

Hence, $e=\frac{c}{a}=\frac{3}{5}$