1. **Problem statement:** We have two concentric circles with radii 2 cm and 4 cm. We need to find the area of the shaded region between the two circles. 2. **Formula used:** The area of a circle is given by $$A = \pi r^2$$ where $r$ is the radius. 3. **Step 1:** Calculate the area of the larger circle with radius 4 cm: $$A_{large} = \pi \times 4^2 = 16\pi$$ 4. **Step 2:** Calculate the area of the smaller circle with radius 2 cm: $$A_{small} = \pi \times 2^2 = 4\pi$$ 5. **Step 3:** Find the area of the shaded region by subtracting the smaller circle's area from the larger circle's area: $$A_{shaded} = 16\pi - 4\pi = (16 - 4)\pi = 12\pi$$ 6. **Final answer:** The area of the shaded region is $$12\pi \text{ cm}^2$$.