Question

What moon phase occurs 3-4 days after a waning gibbous?

Answer 1

The "waning gibbous" begins immediately after the Full Moon and lasts about a week.

At the end of the week, the moon is no longer gibbous, but it's still waning.  At the instant it's exactly half-illuminated, it's called "Third Quarter", and then it continuous to wane for another week.

So 3 to 4 days after the END of the waning gibbous phase, it's a Waning Crescent. It still has another 3 to 4 days of waning to go, before it wanes away to nothing and we have the next New Moon.