1. **State the problem:** We need to find the area of a circle with a diameter of 16 mm. 2. **Recall the formula for the area of a circle:** $$A = \pi r^2$$ where $r$ is the radius of the circle. 3. **Find the radius:** The radius is half the diameter. $$r = \frac{16}{2} = 8 \text{ mm}$$ 4. **Substitute the radius into the area formula:** $$A = \pi \times 8^2$$ 5. **Calculate the square of the radius:** $$8^2 = 64$$ 6. **Write the final answer:** $$A = 64\pi \text{ mm}^2$$ So, the area of the circle is $64\pi$ square millimeters.