Explanation

(b)
Given, $2ae = 8$ and $\frac{2a}{e} = 6 \Rightarrow 2a = 6e$
$\therefore\ e^{2} = \frac{8}{6}\ \Rightarrow \ \ e = \frac{2}{\sqrt{3}}$
$\Rightarrow \ \frac{4}{\sqrt{3}}a = 8\ \Rightarrow \ a = 2\sqrt{3}$
and $b^{2} = a^{2}\left( e^{2} - 1 \right) = 12\left( \frac{4}{3} - 1 \right) = 4$
$\therefore Length\ of\ latusrectum = \frac{2b^{2}}{a} = \frac{2 \times 4}{2\sqrt{3}} = \frac{4}{\sqrt{3}}$