What direction relative to an observer on the earths surface does the moon travel in its orbit?
In this case, there is ‘true’ motion, and there is ‘apparent’ motion. To an observer on earth, the moon ‘appears’ to rise in the east and set in the west, just like the sun. But in fact the moon travels from west to east in its orbit around the earth. From a perspective far about the earth and to the north, the moon travels counter-clockwise around the earth. It is the relatively rapid daily spin of the earth from west to east that causes the apparent motion. The moon takes a whole month to orbit earth; in that time 27+ days have gone by on earth.