The correct distinction between a waxing crescent and a waning gibbous is as follows:
- A waxing crescent occurs after the new moon and before the first quarter (during the first quarter phase leading up to the full moon).
- A waning gibbous occurs after the full moon and before the last quarter (during the third quarter phase leading down to the new moon).
So, the best response would be: "waxing crescent occurs during the second quarter; waning gibbous occurs during the third quarter."