1. **State the problem:** Evaluate the integral $$\int \frac{2}{3x^2} \, dx$$. 2. **Rewrite the integral:** We can rewrite the integrand as $$\frac{2}{3x^2} = \frac{2}{3} x^{-2}$$. 3. **Recall the power rule for integration:** For any real number $n \neq -1$, $$\int x^n \, dx = \frac{x^{n+1}}{n+1} + C$$. 4. **Apply the power rule:** Here, $n = -2$, so $$\int \frac{2}{3} x^{-2} \, dx = \frac{2}{3} \int x^{-2} \, dx = \frac{2}{3} \cdot \frac{x^{-2+1}}{-2+1} + C = \frac{2}{3} \cdot \frac{x^{-1}}{-1} + C$$. 5. **Simplify the expression:** $$= \frac{2}{3} \cdot (-x^{-1}) + C = -\frac{2}{3x} + C$$. **Final answer:** $$\int \frac{2}{3x^2} \, dx = -\frac{2}{3x} + C$$.