1. **State the problem:** Simplify the expression $$\frac{4r}{5r^2} - \frac{2}{3r}$$. 2. **Rewrite each term:** $$\frac{4r}{5r^2} = \frac{4}{5r}$$ because $r$ in numerator and denominator cancels one $r$. 3. **Find common denominator:** The denominators are $5r$ and $3r$. The least common denominator (LCD) is $$15r$$. 4. **Rewrite each fraction with LCD:** $$\frac{4}{5r} = \frac{4 \times 3}{5r \times 3} = \frac{12}{15r}$$ $$\frac{2}{3r} = \frac{2 \times 5}{3r \times 5} = \frac{10}{15r}$$ 5. **Subtract the fractions:** $$\frac{12}{15r} - \frac{10}{15r} = \frac{12 - 10}{15r} = \frac{2}{15r}$$ 6. **Final answer:** $$\boxed{\frac{2}{15r}}$$