Answer
$(-\infty,\infty)$.
The graph is shown below.
Work Step by Step
The given expression is
$\Rightarrow \left | x+4\right |\gt-12$
Rewrite the inequality without absolute value bars.
$\Rightarrow x+4\lt-(-12)$ or $x+4\gt-12$
Solve each inequality separately.
$\Rightarrow x+4\lt12$ or $x+4\gt-12$
Subtract $4$ from all sides.
$\Rightarrow x+4-4\lt12-4$ or $x+4-4\gt-12-4$
Simplify.
$\Rightarrow x\lt8$ or $x\gt-16$
The solution set is less than $8$ or greater than $-16$.
The interval notation is
$(-\infty,8)\cup(-16,\infty)=(-\infty,\infty)$.
