Explanation

(c)
Given equation of ellipse is $\frac{x^{2}}{4} + \frac{y^{2}}{9} = 1$
Here, $a^{2} = 4,\ b^{2} = 9 \Rightarrow b > a$
$\mathbf{\therefore}4 = 9\left( 1 - e^{2} \right) \Rightarrow e = \frac{\sqrt{5}}{3}$
Distance between the directrices $= \frac{2b}{e}$
$= \frac{2 \times 3 \times 3}{\sqrt{5}} = \frac{18}{\sqrt{5}}$