1. **State the problem:** Solve the equation $4 - \frac{3}{5}m = \frac{6}{5}m + 2$ for $m$. 2. **Isolate the variable terms:** Move all terms involving $m$ to one side and constants to the other. $$4 - 2 = \frac{6}{5}m + \frac{3}{5}m$$ 3. **Simplify constants and combine like terms:** $$2 = \frac{6}{5}m + \frac{3}{5}m = \frac{6+3}{5}m = \frac{9}{5}m$$ 4. **Solve for $m$ by dividing both sides by $\frac{9}{5}$:** $$m = \frac{2}{\frac{9}{5}} = 2 \times \frac{5}{9} = \frac{10}{9}$$ 5. **Intermediate step showing cancellation:** $$m = \frac{\cancel{2} \times 5}{\cancel{9}} = \frac{10}{9}$$ 6. **Final answer:** $$m = \frac{10}{9}$$