Why can people tell whether the eastern half is the last quarter moon?

This is the top view. If it is the first quarter moon, (see the red part in the picture) you are on the earth. Look over, the bright side of the moon faces your right hand side. Like a D. on the right is the west, the direction of the sun setting. .

The first quarter moon, (see the blue one, you can also see that the picture below has turned 180 degrees). When you look at the earth, the bright side of the moon is on your left, like a C, and the left side is the east, the direction in which the sun comes out.