1. **State the problem:** Solve the linear equation $2x - 2y = 12$ for $y$ in terms of $x$. 2. **Formula and rules:** To isolate $y$, we need to rearrange the equation by moving terms and dividing both sides by the coefficient of $y$. 3. **Isolate $y$:** $$2x - 2y = 12$$ Subtract $2x$ from both sides: $$-2y = 12 - 2x$$ 4. **Divide both sides by $-2$ to solve for $y$:** $$y = \frac{12 - 2x}{-2}$$ Show cancellation: $$y = \frac{\cancel{12} - \cancel{2}x}{\cancel{-2}}$$ 5. **Simplify the fraction:** $$y = -6 + x$$ 6. **Final answer:** $$y = x - 6$$ This means for any value of $x$, $y$ is $6$ less than $x$.