The formula for the circumference \( C \) of a circle is given by:
\[ C = \pi \times d \]
where \( d \) is the diameter of the circle. Given that the diameter \( d = 4 \) feet, we can calculate the circumference:
\[ C = \pi \times 4 \approx 3.14 \times 4 \approx 12.56 \text{ feet} \]
Among the options provided (6 feet, 13 feet, 25 feet, 50 feet), the best estimation for the circumference of the circle is 13 feet.