1. **State the problem:** Find the length of the longest segment that can fit into a cube with side length 4 cm. 2. **Formula used:** The longest segment inside a cube is its space diagonal, which can be found using the formula for the diagonal of a cube: $$d = s\sqrt{3}$$ where $s$ is the side length of the cube. 3. **Calculate the diagonal:** Given $s = 4$ cm, $$d = 4\sqrt{3}$$ 4. **Explanation:** This formula comes from the Pythagorean theorem applied in three dimensions. The diagonal spans from one corner of the cube to the opposite corner, passing through the interior. 5. **Final answer:** The longest segment that can fit into the cube is $$4\sqrt{3}$$ cm.