Well, technically it only lasts for a short instant when the moon is exactly between the Sun and the Earth, but to our eyes it can appear to last a few days.
When the moon has already past full moon stage, and is again at "half moon" stage, that is last quarter, about 21 days after new moon.
The last couple of nights before New Moon. Or to put it another way, the last few days of the lunar month.
If I'm interpreting your question correctly, there are three phases like that. First is the waning gibbous, which comes after the full moon and lasts until the last quarter, also known as the half moon. That's the second one, the last quarter, and the third is the waning crescent, which lasts from the half moon to the new moon.
14.77 days
The moon is a waxing crescent from the moment of New Moon until the moment of First Quarter. That's 1/4 of its cycle of 29.531 days, which is 7.383 days . . . roughly a week.
The New Moon occurs 29.53 days after the last New Moon.
41 days have passed since the last new moon because April 14 was the last new moon.
In 10 days
The time from New Moon to Last Quarter is 22.15 days.
22.148 days after the New Moon, and 7.383 days after the Full Moon. (figures are rounded)
29.53 days after the last one
When the moon has already past full moon stage, and is again at "half moon" stage, that is last quarter, about 21 days after new moon.
One lunar month is 29.53 days, the time taken from one new moon to the next. The first quarter is 7.3825 days from the new moon phase, one quarter of the lunar month. That's about 7 days and 8 hours.
1st quarter moon . . . 7.38 days after New Moon Full moon . . . 14.77 days after New Moon 3rd quarter moon . . . 22.15 days after New Moon New Moon . . . 29.53 days after the previous New Moon.
It was only Three days
29.53 days after the last one.
The last couple of nights before New Moon. Or to put it another way, the last few days of the lunar month.