1. **State the problem:** Solve the equation $$7 - 2 \cdot (3y + 4) = 5 - 4y$$ for $y$. 2. **Apply the distributive property:** Multiply $-2$ by each term inside the parentheses. $$7 - 2 \cdot 3y - 2 \cdot 4 = 5 - 4y$$ which simplifies to $$7 - 6y - 8 = 5 - 4y$$ 3. **Combine like terms on the left side:** $$7 - 8 = -1$$ so the equation becomes $$-6y - 1 = 5 - 4y$$ 4. **Add $6y$ to both sides to get all $y$ terms on the right:** $$\cancel{-6y} - 1 + 6y = 5 - 4y + 6y$$ which simplifies to $$-1 = 5 + 2y$$ 5. **Subtract 5 from both sides to isolate the $y$ term:** $$-1 - 5 = 5 - 5 + 2y$$ which simplifies to $$-6 = 2y$$ 6. **Divide both sides by 2 to solve for $y$:** $$\frac{-6}{\cancel{2}} = \frac{2y}{\cancel{2}}$$ which simplifies to $$y = -3$$ **Final answer:** $$y = -3$$