Which phase comes straight after the waxing gibbous moon?

The Moon seems to change shape from night to night, but the Moon itself does not change. What changes is our view of it.

The Moon makes no light of its own; it shines because it reflects light from the Sun. At any moment, the Sun lights up one half of the Moon, the half that faces the Sun. As the Moon travels round the Earth, we see different amounts of that lit half, and these are the Moon's phases.

The cycle has eight phases. At new moon, the side facing us is dark and we cannot see the Moon at all. Then a thin waxing crescent appears, followed by the first quarter, when half of the Moon's face is lit, and then a waxing gibbous moon, more than half lit. At full moon we see the whole of the lit side. After that the lit part shrinks again, through waning gibbous, third quarter and waning crescent, until the next new moon. "Waxing" means growing and "waning" means shrinking.

The Moon takes about 27.3 days to go once round the Earth. The time from one new moon to the next is a little longer: about 29.5 days.