1. **State the problem:** Solve for $m$ in the equation $$\frac{4-3}{5}m = \frac{6}{5}(m+2).$$ 2. **Write the equation clearly:** $$\frac{1}{5}m = \frac{6}{5}(m+2)$$ because $4-3=1$. 3. **Multiply both sides by 5 to eliminate denominators:** $$\cancel{5} \times \frac{1}{\cancel{5}} m = \cancel{5} \times \frac{6}{\cancel{5}} (m+2)$$ which simplifies to $$m = 6(m+2).$$ 4. **Distribute 6 on the right side:** $$m = 6m + 12.$$ 5. **Bring all terms involving $m$ to one side:** $$m - 6m = 12$$ which simplifies to $$-5m = 12.$$ 6. **Divide both sides by $-5$ to solve for $m$:** $$m = \frac{12}{-5} = -\frac{12}{5}.$$ **Final answer:** $$m = -\frac{12}{5}.$$