If the distance between the foci of an ellipse is 6 and

Given $2 \mathrm{ae}=6 \Rightarrow \mathrm{ae}=3$ ................(1)

and $\frac{2 a}{e}=12 \Rightarrow a=6 e ...............(2)

from (1) and (2)

$6 \mathrm{e}^{2}=3 \Rightarrow \mathrm{e}=\frac{1}{\sqrt{2}}$

$\Rightarrow a=3 \sqrt{2}$

Now, $b^{2}=a^{2}\left(1-e^{2}\right)$

$\Rightarrow \mathrm{b}^{2}=18\left(1-\frac{1}{2}\right)=9$

Length of L.R $=\frac{2(9)}{3 \sqrt{2}}=3 \sqrt{2}$