Why Do We See A 1/4 Moon Or Half Moon Phase During Day Light Hours And Not A Full Moon?

You haven't paid enough attention to the phases of the moon to notice that today, for instance, you WILL see a full moon in the daytime sky. The moon has a rotation of its own, as it revolves around the earth. Sometimes, you won't see a moon at all in the night sky. That is because in that particular phase, it is rising and setting in the day. The moon is in the sky for 12 hours each day. If it rises in the east at 5 a.m., it sets in the west at 5 p.m., and you may miss it altogether. It takes 28 days and change for the moon to rotate around the earth. If you start with a full moon, or a new moon (one extreme or another), you'll notice that the moon rises about an hour later every day. Look in the weather section of your local paper and check on the moon's rising and setting times. They have nothing to do with the way we see the moon as a quarter or half-moon. The times have to do with the rising and setting of the moon in the phase it is in at that time. So a full moon can rise and the same full moon can set. It can occur in the daytime or the nighttime.

A full moon is always on the opposite side of the earth from the sun. At the latitudes where most of us live, you will never see them in the same sky.

To get an idea how this works, hold a spherical object up in front of you when you are looking at a light. You will notice that you cannot see the entire disk illuminated unless you hold the object behind the light source, or turn around and put yourself between it and the light. Since the moon is closer than the sun, the "behind the light source" option is not possible.

You should study out the moons phases. It is not rocket science. The changing face of the moon is caused by the relative positions of the sun, moon and earth as they change with each lunar cycle.  At any time it is only half of the moon that is lit up by the sun. When the moon is between us and the sun (new moon) then the dark side is facing us and so we cannot see it. Within the next two weeks different size "crescents "will begin to show on its way to half and then full, which is when we can see the fully sunlit side because it is on the opposite side of the earth from the sun and therefore its fully lit side is directly facing us. Full moon then will more or less rise as the sun sets. But half moon will have risen long before and the new moon will travel across the sky during the day.along with the sun. Sometimes both these  are in a direct line with reference to our earth.  Indeed that is why a solar eclipse happens when the new moon "crosses" the face of the sun. It is easy to visualise all this out in your head or on a diagram.