If the mine winch drum diameter is 6cm calculate how far the counterweight will lift for each single rotation of the drum, use the formula c=2cm

You have the formula, though it is incorrect, so fix it and use it.

If you don't know why to use the formula, you just don't understand the problem.
One turn of the wheel uses up enough rope to wrap around the circumference of the drum.
The formula gives you that circumference.

Every day I see this problem stated incorrectly.

I wonder if some textbook has a typo.

English learners in South Africa, I think.

To calculate how far the counterweight will lift for each single rotation of the drum, we can use the formula for the circumference of a circle, which is:

Circumference = 2 * pi * radius

Given that the drum diameter is 6cm, we can find the radius by dividing the diameter by 2:

radius = 6cm / 2 = 3cm

Using the value of pi ≈ 3.14159, we can calculate the circumference as follows:

Circumference = 2 * 3.14159 * 3cm ≈ 18.8496cm

Therefore, for each single rotation of the drum, the counterweight will lift approximately 18.8496cm.