1. **State the problem:** We need to find the area of a right trapezoid with the top base $3$ units, the bottom base $2$ units, and the height $6$ units. 2. **Formula for the area of a trapezoid:** $$\text{Area} = \frac{(\text{base}_1 + \text{base}_2)}{2} \times \text{height}$$ 3. **Identify the bases and height:** - Top base $= 3$ - Bottom base $= 2$ - Height $= 6$ 4. **Substitute the values into the formula:** $$\text{Area} = \frac{(3 + 2)}{2} \times 6$$ 5. **Simplify the expression:** $$\text{Area} = \frac{5}{2} \times 6 = \frac{5 \times 6}{2} = \frac{30}{2} = 15$$ 6. **Conclusion:** The area of the trapezoid is $15$ square units.