1. **State the problem:** Solve the linear equation $3x - 2y = 12$ for $y$ in terms of $x$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation. This involves moving terms and dividing by the coefficient of $y$. 3. **Isolate $y$:** $$3x - 2y = 12$$ Subtract $3x$ from both sides: $$-2y = 12 - 3x$$ 4. **Divide both sides by $-2$ to solve for $y$:** $$y = \frac{12 - 3x}{-2}$$ Show cancellation of the negative sign: $$y = \frac{\cancel{12} - 3x}{\cancel{-2}} = -\frac{12}{2} + \frac{3x}{2}$$ 5. **Simplify the fractions:** $$y = -6 + \frac{3}{2}x$$ 6. **Rewrite in standard form:** $$y = \frac{3}{2}x - 6$$ **Final answer:** $$y = \frac{3}{2}x - 6$$