The lighted half of the moon is always facing the sun.
The entire dark half of the moon is facing earth at the time of "New Moon".
If the hemisphere that is 'lit' is facing away from the earth then it is a new moon
in the new moon, the lighted half of the moon is facing the sun and tha dark side faces the earth.
During the entire two weeks from First Quarter to Third Quarter, more of the moon's lighted surface faces toward Earth than faces away from it.
crescent moon
the lighted half is facing towards the sun not the earth
One half of the moon, the side that faces the Sun, is always lighted. But we usually see only part of the lighted side (phases) as the Moon orbits the Earth. When the Moon is directly between the Earth and the Sun (a new moon) none of the lighted side, facing the Sun, is visible from Earth.
new moon
new moon
The new moon appears dark in the sky because the side of the moon facing Earth is not illuminated by the sun. During this phase, the moon is located between the Earth and the sun, so the side of the moon that is lit is facing away from us, making it seem dark.
At the phase known as the "new moon" none of the illuminated half of the Moon is visible from Earth.One half of the moon, the side that faces the Sun, is always lighted. But we usually see only part of the lighted side (phases) as the Moon orbits the Earth. When the Moon is directly between the Earth and the Sun (a new moon) none of the lighted side, facing the Sun, is visible from Earth.
The new moon phase occurs when the moon lies between the sun and Earth, with the side facing Earth in shadow. This position causes the moon to be not visible from Earth as the illuminated side faces away.
Wow! Let's see if we can sort this out. The problem is the phrase "half side". Half of the moon's surface is always illuminated by the sun. You can call that 50% "the lit side". When the entire lit side is facing the Earth, we see a Full Moon. We see only 1/2 of the lit side one week after a New Moon and again one week before the next New Moon. The first occasion is called the First Quarter phase, and the second occasion is called the Third Quarter phase.