1. **State the problem:** Simplify the expression $$\left(\frac{-8x^2}{-4x^3}\right)$$ and verify it equals $$2x \boxed{1}$$. 2. **Recall the formula and rules:** When dividing powers with the same base, subtract the exponents: $$\frac{x^a}{x^b} = x^{a-b}$$. 3. **Simplify the coefficients:** $$\frac{-8}{-4} = \cancel{\frac{-8}{-4}} = 2$$ because the negatives cancel out. 4. **Simplify the variables:** $$\frac{x^2}{x^3} = x^{2-3} = x^{-1} = \frac{1}{x}$$. 5. **Combine the results:** $$2 \times \frac{1}{x} = \frac{2}{x}$$. 6. **Compare with the given expression:** The simplified form is $$\frac{2}{x}$$, which is not equal to $$2x$$. 7. **Conclusion:** The boxed number should be $$\boxed{-1}$$ to indicate the exponent of $$x$$ in the simplified expression $$2x^{-1}$$. **Final answer:** $$\left(\frac{-8x^2}{-4x^3}\right) = 2x^{-1}$$