Step 1: Recall the direction of Earth's rotation.
The Earth spins on its own axis from west to east, this is the same reason the Sun appears to rise in the east and set in the west.
Step 2: Connect rotation to apparent star motion.
Because the observer on the ground is turning along with the Earth from west to east, distant objects in the sky, including stars, appear to move in the opposite direction relative to the observer.
Step 3: State the apparent direction.
This opposite apparent direction is east to west, matching what we actually see stars do through the night.
Step 4: Rule out other options.
Earth does not rotate east to west, that direction is reversed from the truth. Stars themselves do not physically travel across the sky in a single night, the motion we see is due to Earth's spin. The star background does not move west to east, that is again the opposite of the true observed direction.
Final Answer: B) Earth rotates from west to east.