1. **State the problem:** We are given a trapezoid with bases of lengths 2 cm and 4 cm, an area of 9 square centimeters, and a height $h$ to find. 2. **Formula for the area of a trapezoid:** $$\text{Area} = \frac{(\text{base}_1 + \text{base}_2)}{2} \times h$$ 3. **Substitute known values:** $$9 = \frac{(2 + 4)}{2} \times h$$ 4. **Simplify the bases sum:** $$9 = \frac{6}{2} \times h$$ 5. **Simplify the fraction:** $$9 = 3 \times h$$ 6. **Solve for $h$ by dividing both sides by 3:** $$9 = \cancel{3} \times h \div \cancel{3} \Rightarrow h = \frac{9}{3}$$ 7. **Calculate the height:** $$h = 3$$ **Final answer:** The height $h$ of the trapezoid is 3 centimeters.