What time does the moon reach its apex?

Answer 1

I suppose you mean when the Moon reaches its highest point above the horizon.

It mainly depends on where the Moon is in its orbit around Earth.

For example, the Full Moon is seen when the Moon is opposite the Sun in the sky. So, Full Moon is highest around midnight.

At New Moon, the Moon is highest in the sky around noon, because it's near the Sun in the sky. Actually you can't usually see it then, of course, because of the Sun.

So, you can see the Moon at its highest at many different times depending on the phase of the Moon (which depends on where the Moon is in its orbit).

Answer 2

The moon reaches its apex, or highest point in the sky, at different times each night depending on its position in its orbit around Earth. It is not tied to a specific time.