#### Answer

Option (d)

#### Work Step by Step

RECALL:
If $|x| \gt a$, then $x \lt -a$ or $x \gt a$.
(This is named as Theorem 4 on page 132 of this textbook).
Thus, the inequality that is equivalent to $|x| \gt 4$ is:
$x \lt -4$ or $x \gt 4$
This pair of inequalities is in Option (d).