1. **State the problem:** We have a square and a regular hexagon sharing a common side. The perimeter of the square is 24 inches. We need to find the perimeter of the hexagon. 2. **Identify the side length of the square:** The perimeter of a square is given by the formula $$P = 4s$$ where $s$ is the side length. 3. **Calculate the side length of the square:** Given $$P = 24$$, we solve for $s$: $$24 = 4s$$ $$s = \frac{24}{4}$$ $$s = 6$$ inches. 4. **Understand the hexagon properties:** A regular hexagon has 6 equal sides. Since the hexagon shares a side with the square, each side of the hexagon is also 6 inches. 5. **Calculate the perimeter of the hexagon:** Using the formula for the perimeter of a regular polygon $$P = n \times s$$ where $n$ is the number of sides and $s$ is the side length: $$P = 6 \times 6$$ $$P = 36$$ inches. **Final answer:** The perimeter of the hexagon is 36 inches.