1. **State the problem:** Simplify the expression $$\frac{x}{4} + \frac{2y}{3} - \frac{5y}{6} + \frac{4x}{3}$$. 2. **Find a common denominator for the terms involving $x$ and $y$ separately:** - For $x$ terms: denominators are 4 and 3, common denominator is 12. - For $y$ terms: denominators are 3 and 6, common denominator is 6. 3. **Rewrite each term with the common denominator:** - $\frac{x}{4} = \frac{3x}{12}$ - $\frac{4x}{3} = \frac{16x}{12}$ - $\frac{2y}{3} = \frac{4y}{6}$ - $\frac{5y}{6} = \frac{5y}{6}$ 4. **Combine like terms:** - For $x$: $$\frac{3x}{12} + \frac{16x}{12} = \frac{3x + 16x}{12} = \frac{19x}{12}$$ - For $y$: $$\frac{4y}{6} - \frac{5y}{6} = \frac{4y - 5y}{6} = \frac{-y}{6}$$ 5. **Write the simplified expression:** $$\frac{19x}{12} - \frac{y}{6}$$ 6. **Optional: express with a common denominator 12:** $$\frac{19x}{12} - \frac{2y}{12} = \frac{19x - 2y}{12}$$ **Final answer:** $$\frac{19x - 2y}{12}$$