1. **State the problem:** We need to find the area of a trapezoid with bases 6 cm and 4 cm, and height 2 cm. 2. **Recall the formula for the area of a trapezoid:** $$A = \frac{1}{2} (b_1 + b_2) h$$ where $b_1$ and $b_2$ are the lengths of the two parallel sides (bases), and $h$ is the height. 3. **Identify the values:** - $b_1 = 6$ cm - $b_2 = 4$ cm - $h = 2$ cm 4. **Substitute the values into the formula:** $$A = \frac{1}{2} (6 + 4) \times 2$$ 5. **Simplify inside the parentheses:** $$A = \frac{1}{2} \times 10 \times 2$$ 6. **Multiply:** $$A = \frac{1}{2} \times 20$$ 7. **Simplify the multiplication:** $$A = \cancel{\frac{1}{2}} \times \cancel{20} = 10$$ 8. **Final answer:** The area of the trapezoid is $10$ square centimeters. Note: The equation $6 \times d = 8$ and its solution $d = \frac{40}{6} = \frac{4}{3}$ is unrelated to the trapezoid area calculation but was given in the problem statement.