1. **State the problem:** Simplify the expression for the area of the shaded region, which is the area of the larger rectangle minus the area of the smaller rectangle inside it. 2. **Write the formulas for the areas:** - Area of larger rectangle = length \times width = $$(3x + 2)(4x)$$ - Area of smaller rectangle = length \times width = $$3x \times 2x$$ 3. **Calculate each area:** - Larger rectangle area: $$ (3x + 2)(4x) = 3x \times 4x + 2 \times 4x = 12x^2 + 8x $$ - Smaller rectangle area: $$ 3x \times 2x = 6x^2 $$ 4. **Find the shaded area by subtracting the smaller area from the larger area:** $$ 12x^2 + 8x - 6x^2 $$ 5. **Simplify the expression:** $$ 12x^2 - 6x^2 + 8x = 6x^2 + 8x $$ 6. **Final answer:** The expression for the area of the shaded region in simplest form is: $$\boxed{6x^2 + 8x}$$