1. **State the problem:** Solve the equation $$2(y + 8) = 3(y - 6)$$ for $y$. 2. **Use the distributive property:** Multiply out the parentheses. $$2y + 16 = 3y - 18$$ 3. **Isolate variable terms on one side:** Subtract $2y$ from both sides. $$\cancel{2y} + 16 = 3y - 18 - \cancel{2y}$$ which simplifies to $$16 = y - 18$$ 4. **Isolate $y$:** Add 18 to both sides. $$16 + 18 = y - 18 + 18$$ which simplifies to $$34 = y$$ 5. **Final answer:** $$y = 34$$ The correct choice is 34.