1. **State the problem:** Solve the equation $-9y + 46 = -2(y - 2)$ for $y$. 2. **Apply the distributive property:** Expand the right side: $$-9y + 46 = -2y + 4$$ 3. **Isolate variable terms on one side:** Add $9y$ to both sides: $$\cancel{-9y} + 46 + 9y = -2y + 4 + 9y$$ $$46 = 7y + 4$$ 4. **Isolate the constant term:** Subtract 4 from both sides: $$46 - 4 = 7y + \cancel{4} - 4$$ $$42 = 7y$$ 5. **Solve for $y$:** Divide both sides by 7: $$\frac{42}{\cancel{7}} = \frac{7y}{\cancel{7}}$$ $$6 = y$$ **Final answer:** $$y = 6$$