To find the circumference of Circle B, we can use the formula for the circumference of a circle, which is:
\[ C = 2\pi r \]
where \( C \) is the circumference and \( r \) is the radius.
Given that Circle B has a radius of 60 millimeters, we can substitute that value into the formula:
\[ C_B = 2\pi(60) \]
Calculating this gives:
\[ C_B = 120\pi \]
Using the approximation of \(\pi \approx 3.14\), we can calculate \(C_B\):
\[ C_B \approx 120 \times 3.14 \approx 376.8 \text{ millimeters} \]
Therefore, the approximate circumference of Circle B is:
\[ \boxed{376.8 \text{ mm}} \]