1. **State the problem:** Simplify the expression $$\frac{4x}{3y} - \frac{5y}{6x}$$. 2. **Find a common denominator:** The denominators are $3y$ and $6x$. The least common denominator (LCD) is $$6xy$$. 3. **Rewrite each fraction with the LCD:** $$\frac{4x}{3y} = \frac{4x \times 2x}{3y \times 2x} = \frac{8x^2}{6xy}$$ $$\frac{5y}{6x} = \frac{5y}{6xy}$$ (already has denominator $6xy$) 4. **Subtract the fractions:** $$\frac{8x^2}{6xy} - \frac{5y^2}{6xy} = \frac{8x^2 - 5y^2}{6xy}$$ 5. **Final simplified expression:** $$\boxed{\frac{8x^2 - 5y^2}{6xy}}$$ This is the simplified form of the original expression.