1. **State the problem:** Simplify the expression $$\frac{2 \cdot x \cdot x \cdot x - 8 \cdot x \cdot x \cdot x}{2 \cdot x}$$. 2. **Rewrite the expression:** The numerator is $$2x^3 - 8x^3$$ and the denominator is $$2x$$. 3. **Factor the numerator:** $$2x^3 - 8x^3 = (2 - 8)x^3 = -6x^3$$ 4. **Rewrite the fraction:** $$\frac{-6x^3}{2x}$$ 5. **Simplify the fraction by dividing numerator and denominator by common factors:** $$\frac{\cancel{2} \cdot (-3) \cdot x^{\cancel{1}} \cdot x^{2}}{\cancel{2} \cdot x^{\cancel{1}}} = \frac{-3x^2}{1} = -3x^2$$ 6. **Final answer:** $$-3x^2$$