It takes about 27 days for the moon to orbit Earth once. (Option B).
Why does moon go through phases?
The moon goes through phases because of its orbit around Earth. As the moon orbits Earth, different portions of its illuminated half are visible from Earth, creating the various moon phases.
This cycle, known as the lunar month or synodic month, takes about 27 days to complete. The time it takes for the moon to rotate on its axis (answer A) is also about 27 days, but the key factor for moon phases is its orbit around Earth.
The moon's orbit around the sun (answer C) takes about 27 days as well, but the primary factor for moon phases is its orbit around Earth.