What are the relative positions of the sun, Earth, and moon at the times of lunar and solar eclipses, as well as new, first-quarter, full, and last-quarter phases of the moon?

[2] First Quarter: When the Earth-Moon line is ${90}^{o}$ away from the Earth-Sun line, it is the First Quarter phase. On those days Moon rises (approximately) $6$ hours after the Sun rise and exactly one quarter of the Moon's surface is visible from Earth.
[3] Full Moon: Moon, Earth and Sun lined up with the Earth coming between the Moon and the Sun. But usually the alignment is not perfect with the Moon's longitude lying a little above or below the Sun's longitude. The Earth-Moon line and the Earth-Sun line are close to ${180}^{o}$ away. However, occasionally the alignment could be near perfect leading to an eclipsing of Moon by the Earth. That is Lunar Eclipse . Not every Full Moon is a Lunar Eclipse but every Full Moon coincides with a Full Moon. On Full Moon days Moon rises just as the Sun sets.
[4] Third Quarter: When the Earth-Moon line is ${270}^{o}$ away from the Earth-Sun line, it is the Third Quarter phase. On these days Moon rises (approximately) 18 hours after the Sun rise or (approximately) $6$ hours after the Sun set and again exactly one quarter of the Moon's surface is visible from Earth.