1. **State the problem:** Solve the equation $6 + \frac{y}{3} = 2(1 + y)$ for $y$. 2. **Write the equation:** $$6 + \frac{y}{3} = 2(1 + y)$$ 3. **Distribute the right side:** $$6 + \frac{y}{3} = 2 + 2y$$ 4. **Subtract 2 from both sides:** $$6 - 2 + \frac{y}{3} = 2y$$ $$4 + \frac{y}{3} = 2y$$ 5. **Subtract $\frac{y}{3}$ from both sides:** $$4 = 2y - \frac{y}{3}$$ 6. **Combine like terms on the right side:** $$2y - \frac{y}{3} = \frac{6y}{3} - \frac{y}{3} = \frac{5y}{3}$$ So, $$4 = \frac{5y}{3}$$ 7. **Multiply both sides by 3 to clear the denominator:** $$4 \times 3 = 5y$$ $$12 = 5y$$ 8. **Divide both sides by 5 to solve for $y$:** $$y = \frac{12}{5}$$ **Final answer:** $$y = \frac{12}{5}$$