Final answer:
A star can have an apparent magnitude of 12 and an absolute magnitude of -2 because it is very bright inherently (absolute), but appears faint from Earth (apparent) due to being far away.
Step-by-step explanation:
A star can have an apparent magnitude of 12 and an absolute magnitude of -2 because apparent magnitude measures how bright a star appears from Earth, while absolute magnitude measures how bright a star would appear at a standard distance of 10 parsecs. The significant difference between the apparent and absolute magnitudes indicates that the star is relatively far from Earth but intrinsically very bright. If the star were closer, its apparent magnitude would be brighter (a lower number), and if the star were not very bright, its absolute magnitude would be higher (a less negative or a positive number).
The correct answer to the question is c) The star is relatively far from Earth and very bright. An absolute magnitude of -2 signifies a very luminous star, but its high apparent magnitude number shows that it appears dimmer to us due to its large distance from Earth. Therefore, although the star is very luminous, it appears faint due to the inverse-square law, which dictates that the brightness of a star decreases with the square of the distance from the observer.