1. **State the problem:** Simplify the expression $-\frac{62}{6} + 4 + \frac{32}{3} + 8$. 2. **Find a common denominator:** The denominators are 6 and 3. The least common denominator (LCD) is 6. 3. **Rewrite all terms with denominator 6:** $4 = \frac{4 \times 6}{6} = \frac{24}{6}$ $\frac{32}{3} = \frac{32 \times 2}{3 \times 2} = \frac{64}{6}$ $8 = \frac{8 \times 6}{6} = \frac{48}{6}$ 4. **Rewrite the entire expression:** $$-\frac{62}{6} + \frac{24}{6} + \frac{64}{6} + \frac{48}{6}$$ 5. **Combine all fractions:** $$\frac{-62 + 24 + 64 + 48}{6} = \frac{74}{6}$$ 6. **Simplify the fraction:** $$\frac{74}{6} = \frac{\cancel{2} \times 37}{\cancel{2} \times 3} = \frac{37}{3}$$ 7. **Final answer:** $$\boxed{\frac{37}{3}}$$