1. The problem is to find the area of a trapezoid with the top base $2$ m, bottom base $6$ m, and height $4$ m. 2. The formula for the area $A$ of a trapezoid is: $$A = \frac{(b_1 + b_2)}{2} \times h$$ where $b_1$ and $b_2$ are the lengths of the two bases, and $h$ is the height. 3. Substitute the given values: $$A = \frac{(2 + 6)}{2} \times 4$$ 4. Simplify inside the parentheses: $$A = \frac{8}{2} \times 4$$ 5. Simplify the fraction: $$A = 4 \times 4$$ 6. Multiply to find the area: $$A = 16$$ 7. Therefore, the area of the trapezoid is $16$ square meters.