1. **State the problem:** Simplify the expression $-4(y+1)+2$. 2. **Apply the distributive property:** Multiply $-4$ by each term inside the parentheses. $$-4(y+1) = -4 \times y + (-4) \times 1 = -4y - 4$$ 3. **Rewrite the expression:** Substitute the distributed terms back into the expression. $$-4y - 4 + 2$$ 4. **Combine like terms:** Combine the constants $-4$ and $2$. $$-4y + \cancel{-4} + \cancel{2} = -4y - 2$$ 5. **Final simplified expression:** $$\boxed{-4y - 2}$$ This is the simplified form of the original expression.