The Moon is visible on both sides of the world because its motion is synchronized with the rotation of the Earth. This synchronization is known as tidal locking. Here's how it works:
The Moon takes approximately 29½ days to complete one orbit around the Earth, which is known as its synodic month or lunar month. However, during this time, the Earth also rotates on its axis, completing one full rotation every 24 hours. This rotation of the Earth causes the Moon to appear in different positions in the sky from different locations on Earth.
Although the Moon takes 29½ days to orbit the Earth, it takes roughly the same amount of time (24 hours) for a specific location on Earth to face the Moon again due to the Earth's rotation. This synchronization means that as the Earth spins, different parts of the world come into view of the Moon.
Imagine a person standing at a particular location on Earth, observing the Moon. As the Earth rotates, that person will eventually turn away from the Moon, and someone on the opposite side of the world will turn toward the Moon. This is why the Moon can be visible from different parts of the world at different times, even though it takes longer for the Moon to complete its orbit.
It's worth noting that the Moon's phase (the shape and appearance of the lit portion of the Moon) changes during its orbit, which further adds to the variation in its visibility from different locations on Earth.