Explanation

(a)
$x^{2} - 5|x| + 6 = 0$
$\Rightarrow \ \ \left| x^{2} \right| - 5|x| + 6 = 0$
$\Rightarrow \left( |x| - 2 \right)\left( |x| - 3 \right) = 0$
$\Rightarrow \ \ |x| = 2,\ \ \ \ \ |x| = 3$
$\Rightarrow \ \ \ x = \pm 2,\ \ \ \ \ x = \pm 3$
Hence, the given equation has four solutions