The First Quarter Moon always occurs when A. the Moon is directly opposite the position of the Sun. B. when the Moon is closer to the Sun than the Earth is. C. on the 7th or 8th of every month. D. when the Moon is at right angles to the direction of the Sun.

Option D

When the Moon is at right angles to the direction of the Sun.

Explanation:

The moon does not shine on its own, for example, like the sun that emits light as a consequence of its temperature. Instead, the moon is reflecting the sunlight (that is known as albedo).

The moon orbits the earth in a time 27.3 day, a sidereal period. According to that and the fact the Earth orbits the Sun, the moon will show different phases when is reflecting the sunlight along a month due to the configuration of those three celestial objects (Moon, Earth and the Sun).

When there is a Right angle between the Moon and to the direction of the Sun, half its face will appear to be illuminated in the night sky (that is called First Quarter).

Notice that when the Moon is between the Earth and the Sun it will be illuminated in its back, so it is not possible to see it from the Earth (that is called new moon).

However, a solar eclipse doesn't happens every month since the orbital plane of the moon is not in the same plane as the Earth's orbital plane with respect to the Sun.