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An important thing to note with inequalities is that the inequality always flips when you multiply or divide both sides by a negative.
So you have,
-1/3h ≤ 6
and you multiply both sides by -3 to get
h ≥ -18
You can treat it like an equality usually, but that rule I stated above is important to remember.
[tex]-\frac{1}{3}h\leq6\ \ \ |change\ signs\\\\\frac{1}{3}h\geq-6\ \ \ \ |divide\ both\ sides\ by\ \frac{1}{3}\ (multiply\ both\ sides\ by\ 3)\\\\\boxed{h\geq-18}\to\boxed{h\in[-18;\ \infty)}[/tex]

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