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To determine which lunar phase corresponds with a zenith time of 6 AM, we can analyze the positioning of the Moon and its phases in relation to Earth's rotation and the timing of its appearance in the sky.
The zenith time refers to when the Moon is at its highest point in the sky, which occurs when it is due south. At this point for a moon phase, the Moon will rise approximately six hours before this time and set about six hours after.
In the case of the third quarter phase, which is roughly visible around midnight to early morning hours, it would reach its zenith around 6 AM. This means that if you observe a third quarter Moon at its highest point in the sky at 6 AM, it would have risen around midnight, be due south at 6 AM, and then set later in the morning.
Other phases would be positioned differently in the sky at that time. A full Moon would be visible all night and culminate at midnight, while a waning gibbous would still be high in the sky but would not peak directly overhead at that specific time. The first quarter Moon rises at noon and sets at midnight, so at 6 AM, it would still be located low on the eastern horizon