1. **State the problem:** Simplify the expression $\left(\frac{1}{5}c - 8\right) + \left(-\frac{2}{3}c + 4\right)$. 2. **Write the expression:** $$\frac{1}{5}c - 8 - \frac{2}{3}c + 4$$ 3. **Group like terms:** $$\left(\frac{1}{5}c - \frac{2}{3}c\right) + (-8 + 4)$$ 4. **Find common denominator for coefficients of $c$:** The denominators are 5 and 3, so common denominator is 15. $$\frac{1}{5}c = \frac{3}{15}c, \quad \frac{2}{3}c = \frac{10}{15}c$$ 5. **Subtract coefficients:** $$\frac{3}{15}c - \frac{10}{15}c = \frac{3 - 10}{15}c = -\frac{7}{15}c$$ 6. **Simplify constants:** $$-8 + 4 = -4$$ 7. **Combine results:** $$-\frac{7}{15}c - 4$$ **Final answer:** $$-\frac{7}{15}c - 4$$