1. **Problem Statement:** Nathan is making a kite with two adjacent sides each 12 inches and a right angle between them. We need to find the length of the support rod, which is the diagonal across the kite. 2. **Formula Used:** For a kite with perpendicular adjacent sides, the support rod corresponds to the diagonal formed by these sides. Using the Pythagorean theorem: $$\text{Support rod length} = \sqrt{(12)^2 + (12)^2}$$ 3. **Calculation:** $$= \sqrt{144 + 144}$$ $$= \sqrt{288}$$ 4. **Simplify the square root:** $$= \sqrt{144 \times 2}$$ $$= \sqrt{144} \times \sqrt{2}$$ $$= 12\sqrt{2}$$ 5. **Answer:** The length of the support rod is $12\sqrt{2}$ inches. Therefore, the correct choice is **D. 12√2 inches**.