What is the distance between settlements if the measurement turned out to be 6 cm, and the scale of the map is 1: 10000?

The scale indicates how many centimeters on some terrain will fit in one centimeter on the plan. Therefore, according to the indicated data, a map scale of 1: 10000 means that just one centimeter of terrain corresponds to as many as ten thousand centimeters (1 cm = 10000 cm = 100 m).

Then, 6 cm = 6 x 10,000 = 60,000 cm.

Since one meter contains one hundred centimeters,

60,000 cm = 60,000: 100 = 600 m.

Answer: the distance between settlements is 600 m.