Answer
$n\geq40$ or $n\leq0$
Work Step by Step
$|0.4n-8|+4\geq12\\|0.4n-8|\geq8$ implies $0.4n-8\geq8\\0.4n\geq16\\n\geq40$ or $0.4n-8\leq-8\\0.4n\leq0\\n\leq0$.
Thus $n\geq40$ or $n\leq0$.
Then, by using a graphing utility, the solution set is attached.