1. **State the problem:** Simplify the expression $$\frac{3xy - 6x}{2y} - y^2$$. 2. **Rewrite the expression:** The expression is a fraction minus a term: $$\frac{3xy - 6x}{2y} - y^2$$ 3. **Factor the numerator:** Factor out the common factor $3x$ from the numerator: $$\frac{3x(y - 2)}{2y} - y^2$$ 4. **Split the fraction:** We can write the fraction as: $$\frac{3xy}{2y} - \frac{6x}{2y} - y^2$$ 5. **Simplify each term:** - $$\frac{3xy}{2y} = \frac{3x \cancel{y}}{2 \cancel{y}} = \frac{3x}{2}$$ - $$\frac{6x}{2y} = \frac{6x}{2y} = \frac{3x}{y}$$ 6. **Rewrite the expression:** $$\frac{3x}{2} - \frac{3x}{y} - y^2$$ 7. **Final simplified form:** The expression cannot be combined further without a common denominator, so the simplified expression is: $$\frac{3x}{2} - \frac{3x}{y} - y^2$$