absoulute value(x/3+6) - 8 < -5
$\displaystyle \left | \frac{x}{3} + 6 \right | - 8 \leq -5$
$\displaystyle \left | \frac{x}{3} + 6 \right | \leq 3$
Thus, we know that
$\displaystyle -3 \leq \frac{x}{3} + 6 \leq 3$
Subtracting 6 from "all three sides"
$\displaystyle -9 \leq \frac{x}{3} \leq -3$
Multiplying "all three sides" by 3
$\displaystyle -27 \leq x \leq -9$
-Dan