Explanation

(c)
Given, |$\overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}}| = 4\ \Longrightarrow \left| \overrightarrow{\mathbf{a}} \right||\overrightarrow{\mathbf{b}}|$ $\sin\theta = 4$ …..(i)
$\Longrightarrow \sin\theta = \frac{4}{\left| \overrightarrow{\mathbf{a}} \right||\overrightarrow{\mathbf{b}}|}$
$Alos,\ \left| \overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{b}} \right| = 2\ \ \Longrightarrow \ \ \ \left| \overrightarrow{\mathbf{a}} \right||\overrightarrow{\mathbf{b}}|$ $\cos\theta = 2$
$\Longrightarrow \left| \overrightarrow{\mathbf{a}} \right|^{2}\ \left| \overrightarrow{\mathbf{b}} \right|^{2}\left( 1 - \sin^{2}\theta \right) = 4$
$\ \Longrightarrow \left| \overrightarrow{\mathbf{a}} \right|^{2}\ \left| \overrightarrow{\mathbf{b}} \right|^{2}\left( 1 - \frac{16}{{|\overrightarrow{\mathbf{a}}|}^{2}\ {|\overrightarrow{\mathbf{b}}|}^{2}} \right) = 4\ \ \ \lbrack From\ Eq.1\rbrack$
$\Longrightarrow \ {|\overrightarrow{\mathbf{a}}|}^{2}\ {|\overrightarrow{\mathbf{b}}|}^{2} = 20$