1. **State the problem:** Solve the compound inequality $$-6 \leq \frac{5g - 8}{3} < 4$$ for $g$ and graph the solution on a number line. 2. **Recall the rule:** When solving inequalities involving fractions, multiply all parts of the inequality by the denominator to eliminate the fraction, being careful to maintain inequality directions (multiplying by a positive number does not change inequality signs). 3. **Multiply all parts by 3:** $$-6 \leq \frac{5g - 8}{3} < 4 \implies -6 \times 3 \leq 5g - 8 < 4 \times 3$$ $$-18 \leq 5g - 8 < 12$$ 4. **Add 8 to all parts:** $$-18 + 8 \leq 5g - 8 + 8 < 12 + 8$$ $$-10 \leq 5g < 20$$ 5. **Divide all parts by 5:** $$\frac{-10}{5} \leq \frac{5g}{5} < \frac{20}{5}$$ $$-2 \leq g < 4$$ 6. **Use \cancel to show simplification:** $$\cancel{5}g / \cancel{5} = g$$ $$\frac{\cancel{-10}}{5} = -2$$ $$\frac{20}{\cancel{5}} = 4$$ 7. **Interpretation:** The solution is all $g$ values from $-2$ to $4$, including $-2$ (closed endpoint) but not including $4$ (open endpoint). **Final answer:** $$-2 \leq g < 4$$