1. **State the problem:** Solve the linear equation $y - 2y = 4x + 6$ for $y$. 2. **Simplify the left side:** Combine like terms on the left side. $$y - 2y = \cancel{1y} - \cancel{2y} = -1y = -y$$ So the equation becomes: $$-y = 4x + 6$$ 3. **Isolate $y$:** Multiply both sides by $-1$ to solve for $y$. $$\cancel{-1} \cdot y = \cancel{-1} \cdot (4x + 6)$$ $$y = -4x - 6$$ 4. **Final answer:** The equation solved for $y$ is $$y = -4x - 6$$ This is the slope-intercept form of a linear equation where the slope is $-4$ and the y-intercept is $-6$.