1. **State the problem:** Simplify the expression $$\frac{y^2}{3} - \frac{2}{y}$$. 2. **Identify the common denominator:** To combine the terms, find a common denominator. The denominators are 3 and $y$, so the common denominator is $3y$. 3. **Rewrite each term with the common denominator:** $$\frac{y^2}{3} = \frac{y^2 \cdot y}{3 \cdot y} = \frac{y^3}{3y}$$ $$\frac{2}{y} = \frac{2 \cdot 3}{y \cdot 3} = \frac{6}{3y}$$ 4. **Combine the terms:** $$\frac{y^3}{3y} - \frac{6}{3y} = \frac{y^3 - 6}{3y}$$ 5. **Final simplified expression:** $$\boxed{\frac{y^3 - 6}{3y}}$$ This is the simplified form of the original expression.