What is the only phase of the moon during which a solar eclipse can occur? Why?

Only during the New Moon–Dark Moon phase can it happen.

A total solar eclipse lasts for approximately seven minutes at a specific location because the moon's shadow is (relatively) small. A solar eclipse occurs when the sun, moon, and earth are in (almost) perfect alignment. This only occurs when the sun, as seen from Earth, is at the other side of the moon, 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.

A lunar eclipse occurs only during a full moon, when the sun, earth, and moon are in that order. Because of the earth's larger shadow cone, a lunar eclipse lasts for hours and can be seen from the entire night side of the planet. The eclipsed moon always appears dark red due to reddish light being refracted from the earth's atmosphere.

A solar eclipse can only occur during the new moon phase. This is because during a new moon, the moon is positioned directly between the Earth and the sun, causing its shadow to fall on Earth, resulting in a solar eclipse.