We check each option using the well established fact about the direction Earth spins.
Earth rotating east to west would mean the Sun rises in the west, which contradicts everyday observation, so this option is wrong.
Stars physically moving east to west on their own, in just one night, is not correct, stars are effectively fixed over such a short time, what changes is the observer's own position due to Earth's spin.
The star background moving west to east is the opposite of what is actually observed in the night sky, stars trail from east to west.
Earth actually spins from west to east, so an observer standing on the rotating ground sees the sky, including the stars, drift in the opposite direction, from east to west, throughout the night.
So option B correctly explains the apparent east to west motion of stars.