Explanation

(d)
Given, $\left| x^{2} - x - 6 \right| = x + 2$
Now, we have to consider two cases,
Case I When $x \leq -$ or $x \geq 3$
$\Rightarrow \ \ x^{2} - x - 6 = x + 2$
$\Rightarrow \ \ \ x^{2} - 2x - 8 = 0\ \ \Rightarrow \ \ \ \ x = - 2,\ 4$
Case II When $- 2 < x < 3$
$\Rightarrow \ - \left( x^{2} - x - 6 \right) = x + 2\ \Rightarrow x^{2} = 4\ \Rightarrow x = \pm 2$
Hence, the roots are $( - 2,\ 2,\ 4)$