To calculate the mechanical advantage of a screw, we can use the formula:
\[
\text{Mechanical Advantage} (MA) = \frac{\text{Circumference}}{\text{Pitch}}
\]
Where:
- The **circumference** is the distance covered in one complete revolution of the screw.
- The **pitch** is the distance between adjacent threads.
In this case:
- The circumference of the screw is given as \(2\) centimeters.
- The pitch can be calculated based on the number of threads per centimeter. Since the screw has \(4\) threads per centimeter, the pitch is the reciprocal of that:
\[
\text{Pitch} = \frac{1 \text{ cm}}{4 \text{ threads}} = 0.25 \text{ cm}
\]
Now, substituting the values into the formula for mechanical advantage:
\[
MA = \frac{2 \text{ cm}}{0.25 \text{ cm}} = 8
\]
Thus, the mechanical advantage of the screw is \(8\).
The correct answer is \(\boxed{8}\).