What is responsible for the apparent motion of the moon in the sky from east to west?

As a result, although the Moon is moving to the east relative to the stars, the much faster westward motion of the sky is carrying it to the west, so despite its eastward motion relative to the center of the Earth, it rises in the east and sets in the west, just like any other celestial body.

layer a is the exosphere and layer b is the thermosphere.   is the answer i think but i hope this .