To solve the inequality we have to remember the property:
[tex]\lvert x\rvert\ge a\Leftrightarrow x\ge a\lor x\leq-a[/tex]Then:
[tex]\begin{gathered} 5\lvert x+4\rvert-4\ge36 \\ 5\lvert x+4\rvert\ge40 \\ \lvert x+4\rvert\ge\frac{40}{5} \\ x+4\ge8\lor x+4\leq-8 \\ x\ge8-4\lor x\leq-8-4 \\ x\ge4\lor x\leq-12 \end{gathered}[/tex]Therefore the solution is:
[tex](-\infty,-12\rbrack\cup\lbrack4,\infty)[/tex]