Towards the Earth all or some of the time, I think. Look at the Moon phases/cycle diagram.
a full moon
When the moon is in the general direction of the sun as seen from Earth, then we're looking at the part of it that's not illuminated all by the sun, and we see no moon at all.
waning gibbous
The moon goes in the direction of its orbit
It's still called the Earth
The Moon has no east-west direction with respect to Earth. East-west describes the direction of, or opposite direction of a sphere that is rotating. (Like Earth.) As it turns out, the same side of the Moon always faces the Earth. The phases of the Moon, like full Moon, result from which direction the SUN is from the Moon and Earth.
The Moon always keeps the same side facing the Earth.So, whatever direction you name, there is some place on the Moon from which the Earth appears in that direction, and if the observer doesn't move to a different place on the Moon, then the Earth doesn't move either. It's always in the same direction. The concept of "Earth rise" or "Earth set" does not apply on the Moon.(This video from Apollo 8 came as the spacecraft was circling the Moon in orbit.)Note that for about half of the Moon's surface (the far side), the Earth is never visible. During the full moon, very little of Earth is illuminated by the Sun, as seen from the Moon.
Towards the moon's centre.
The moon's acceleration is expressed as a change in direction.
To see the full moon when it first rises, look toward the eastern horizon. The moon rises in the eastern part of the sky and moves westward as the night progresses.
The moon revolves around the Earth in a counterclockwise direction when viewed from the North Pole.
The direction the moon faces changes throughout the night as it moves across the sky. You can determine the moon's current direction by using a compass or a stargazing app that shows its location in real time.