What is the only phase of the moon during which a solar eclipse can occur? Why?
It can only occur during New Moon - Dark Moon
A solar eclipse is when Sun - Moon - Earth -- IN THAT ORDER are in (almost) perfect alignment. This happens only when the sun (as seen from the earth) is at the other side of the moon, so the sun is lighting the back side and not the side that is turned toward us (i.e. New Moon). The moon then casts its shadow on some part of the earth. And since the earth moves, the shadow also moves. The maximum time for a total solar eclipse at a certain location is around 7 minutes, because the shadow of the moon is (relatively) small.
A lunar eclipse is when the order is Sun - Earth - Moon, so this happens only at Full Moon. The shadow-cone of the earth is much larger, so a lunar eclipse lasts for hours AND is visible from the whole night-side of the earth. Almost always some reddish light is refracted from the earth's atmosphere to give the eclipsed moon a dark red appearance.