1. **State the problem:** We need to find the area of a trapezoid with top base $6$ mm, bottom base $8$ mm, and height $4$ mm. 2. **Formula for the area of a trapezoid:** $$\text{Area} = \frac{(\text{Base}_1 + \text{Base}_2)}{2} \times \text{Height}$$ 3. **Apply the values:** $$\text{Area} = \frac{(6 + 8)}{2} \times 4$$ 4. **Simplify inside the parentheses:** $$6 + 8 = 14$$ 5. **Calculate the average of the bases:** $$\frac{14}{2} = 7$$ 6. **Multiply by the height:** $$7 \times 4 = 28$$ 7. **Conclusion:** The area of the trapezoid is $28$ square millimeters.