Answer
Interval Notation: $(-∞,-4)∪(4,∞)$
Graph:
Work Step by Step
$|x| +2 \gt 6$
To isolate the absolute value expression, add $-2$ to both sides of the inequality.
$|x| +2 -2 \gt 6-2$
$|x| \gt 4 $
By [$|X| \gt a = X \lt -a $ or $X \gt a$ ] property,
$|x| \gt 4 $ is equivalent to $x \lt -4 $ or $ x \gt 4$
Interval Notation: $(-∞,-4)∪(4,∞)$