1. **State the problem:** We are given the area of a rectangle as $$6x^3 - 2x^2 + 4x$$ and the width as $$2x$$. We need to find the length of the rectangle. 2. **Formula used:** The area $$A$$ of a rectangle is given by $$A = \text{length} \times \text{width}$$. 3. **Set up the equation:** Let the length be $$L$$. Then, $$6x^3 - 2x^2 + 4x = L \times 2x$$ 4. **Solve for length $$L$$:** Divide both sides by $$2x$$: $$L = \frac{6x^3 - 2x^2 + 4x}{2x}$$ 5. **Simplify the expression:** $$L = \frac{6x^3}{2x} - \frac{2x^2}{2x} + \frac{4x}{2x}$$ 6. **Cancel common factors:** $$L = 3\cancel{x^2} - 1\cancel{x} + 2$$ 7. **Final simplified length:** $$L = 3x^2 - x + 2$$ **Answer:** The length of the rectangle is $$3x^2 - x + 2$$ units.