using thedefinition of absolute value(which I recommend you take another look at in your textbook or other resource)

$\displaystyle |x^2 - 4| = x^2 - 4$ if ($\displaystyle x^2-4) \ge 0$

$\displaystyle |x^2 - 4| = -(x^2 - 4) = 4-x^2$ if $\displaystyle (x^2-4) < 0$

now, which case should be used if $\displaystyle |x^2-4| = 0$ ?