When we can see the Moon during the day, the other side of the world, where it is night, can also see the Moon. The visibility of the Moon does not depend on whether it is day or night in a particular location on Earth.
The Moon orbits around the Earth, and its position in the sky is determined by its phase and its location relative to the Sun and Earth. The phase of the Moon refers to the portion of its illuminated side that is visible from Earth. During a full moon, the entire illuminated side is visible, while during a new moon, the illuminated side is facing away from Earth, making it appear dark.
Regardless of whether it is day or night, people on opposite sides of the world will see the same phase of the Moon at a given time. For example, if it is daytime and you can see a crescent Moon, someone on the opposite side of the world, where it is nighttime, would also see a crescent Moon.
The visibility of the Moon during the day or night is mainly determined by its position relative to the Sun and Earth, as well as atmospheric conditions and the observer's location. However, the phase of the Moon remains the same regardless of the time of day.