1. **State the problem:** Solve the equation $$\frac{2x - 5}{6} - \frac{3x - 4}{8} = 0$$. 2. **Formula and rules:** To solve equations involving fractions, find a common denominator to combine terms or eliminate denominators by multiplying both sides. 3. **Find the least common denominator (LCD):** The denominators are 6 and 8. The LCD is $$24$$. 4. **Multiply both sides of the equation by 24 to clear denominators:** $$24 \times \left(\frac{2x - 5}{6} - \frac{3x - 4}{8}\right) = 24 \times 0$$ 5. **Distribute multiplication:** $$24 \times \frac{2x - 5}{6} - 24 \times \frac{3x - 4}{8} = 0$$ 6. **Simplify each term:** $$\cancel{24}^{4} \times \frac{2x - 5}{\cancel{6}^{1}} - \cancel{24}^{3} \times \frac{3x - 4}{\cancel{8}^{1}} = 0$$ This simplifies to: $$4(2x - 5) - 3(3x - 4) = 0$$ 7. **Expand the terms:** $$8x - 20 - 9x + 12 = 0$$ 8. **Combine like terms:** $$8x - 9x - 20 + 12 = 0$$ $$-x - 8 = 0$$ 9. **Isolate $x$:** $$-x = 8$$ 10. **Divide both sides by -1:** $$\frac{\cancel{-1}x}{\cancel{-1}} = \frac{8}{-1}$$ $$x = -8$$ **Final answer:** $$x = -8$$