1). The waxing gibbous phase represents the portion of the cycle of phases
during which the moon appears more than half but less than fully lit, and is growing
as time goes on. In the picture, it's everything from position-3 to position-5. It's
one fourth of the entire cycle, which is 7.4 days, so you'd see it on 7 or 8 consecutive
(The complete cycle of phases is 29.53 days.)
2). The complete cycle of phases is 29.53 days. Any phase visible on December 21
is visible again on January 19 or January 20.
3). From position-8 to position-5 in the picture is 5/8 of all the way around.
(5/8) of (29.53) = 18.5 days.
4). The locations of high- and low-tides on the Earth are influenced by the position
of the moon and the rotation of the Earth.
5). A lunar eclipse is the result of the moon sailing into the Earth's shadow.
The Earth's shadow is out behind it, opposite to the sun, toward position-5
in the picture, not position-4.