Question: Solve for y: 6(y - \frac{1}{3}) = 4(3y - 5).
1. **State the problem:** Solve the equation $$6\left(y - \frac{1}{3}\right) = 4(3y - 5)$$ for $$y$$.
2. **Distribute both sides:**
$$6y - 6 \times \frac{1}{3} = 12y - 20$$
3. **Simplify the multiplication:**
$$6y - 2 = 12y - 20$$
4. **Bring all $$y$$ terms to one side and constants to the other:**
$$6y - 12y = -20 + 2$$
5. **Simplify both sides:**
$$-6y = -18$$
6. **Divide both sides by $$-6$$ to solve for $$y$$:**
$$y = \frac{-18}{-6}$$
7. **Cancel common factors:**
$$y = \frac{\cancel{-18}}{\cancel{-6}} = 3$$
**Final answer:** $$y = 3$$