In what ways do earth and the moon move through space? how do these motions produce such phenomena as day and night, the seasons, phases of the moon, and eclipses?

Motion always has to be described relative to something ... you have to
name your point of view.

-- To somebody hanging over the north pole in a hot air balloon . . .
     -- the Earth turns under him, once every 23hrs 56minutes.
     -- the Moon sails around the Earth, once every 27.32 days,
         on a path roughly 238,000 miles out.

-- To somebody hanging over the Sun's north pole in a hot air balloon . . .
     -- the Sun turns under him, about once every 30 days.
     -- the Earth sails around him, once a year, on a path about 93 million
          miles out. 
     -- it also spins once every 24 hours.
         The invisible 'pencil' that the Earth spins on is not straight up and
         down.  It's tilted about 23.5 degrees away from it.  So for half of
         the year, the top of the Earth tilts toward the Sun, and the bottom
         tilts toward the Sun for other half of the year.   
     -- the Moon also sails around him, once a year, roughly 238,000
          miles from the Earth, and wiggling slightly nearer and farther
          from the Sun every 2 weeks or so, as much as it has to in order
          to avoid getting in the Earth's way.
     -- The Moon also wiggles slightly above and below the Earth's
           path, so it's hardly ever on the line from Sun the Earth.


-- The Earth spins roughly once every 24 hours.
You can't light up more than half of a ball with a flashlight, so
there's always half of the Earth lit up by the sun and half of it
not lit up.  We call those parts 'day' and 'night'.  The Earth spins,
so the lit-up part and the dark part keep moving to new places.

-- The 'pencil' that the Earth spins on is not straight up and down. 
It's tilted about 23.5 degrees away from there.  So for half the year,
the top of the Earth tilts toward the Sun, and the bottom of it tilts
toward the Sun the other half.  Whichever half tilts toward the Sun
gets more bang out of the sun, and stays generally warmer during
that half year.  The tilt makes the seasons. 
This has nothing to do with how near or far from the Sun it is. 
It's all in the tilt.  Whichever half tilts toward the sun is nearer to the
center of the lit-up half, so the Sun is higher in the sky, shining more
directly on them.

-- The moon is also half lit-up and half dark.  From what we can see,
it looks like it's going around us.
   When the moon is out in front of us (toward the Sun), we can't see
any of the lit-up half.  We're looking at its dark half, so we see nothing.
   When the Moon is straight behind us (away from the Sun), we can
see the entire lit-up half ... the "full" Moon.
   When the Moon is to the side of us, we see half of the lit-up part and
half of the dark part.  It looks to us like half of a light circle.

-- The Earth is sailing around the Sun on a path that's flat, like the edge
of a huge dinner plate.
   The path of the Moon doesn't lie on the surface of the same plate. 
It's tilted a little bit above and below the plate, so that the Moon is
hardly ever exactly on the line between the Sun and Earth.
     When the Moon is out in front of us, its shadow usually misses
falling on the Earth.  And when it's behind us, it's usually above or
below the Earth's shadow.
     BUT ... if the Moon happens to be behind us AND close enough to
the Earth's big dinner plate, then it's full AND it sails straight through
the Earth's shadow.  For a few hours, the Sun can't light up the moon
because the Earth is in the way.  Anybody who can see the Moon sees
it turn dark for a few hours, until it sails out of the Earth's shadow again.
That's a 'lunar eclipse' ... an eclipse of the Moon.
     If the Moon happens to be in front of us AND also close enough to
the Earth's big dinner plate, then we can't see it at all, AND the skinny
tip of its shadow falls on the Earth.  It's only maybe a couple hundred
miles across, and it's moving fast.  But for a few minutes, anybody in
that little spot can't see the Sun ! because the Moon is in the way. 
That's a 'total solar eclipse' ... an eclipse of the Sun.
For a person sitting still in one place, the longest it can ever last is
a little bit over 7 minutes.  People inside that little circle see a pitch
black disk where the Sun should be, with a fiery, sparkling cloudy
fuzzball around it, called the Sun's 'corona'.
   Once the shadow passes ... or for people who were off to the side
and never saw the Sun completely covered ... the Sun looks like part
of it is missing.  It's a crescent Sun ... to me, it looks like a giant cashew
nut in the sky.  It's the Sun, with part of it blocked from our view by the
Moon.  During this process, it's called a 'partial solar eclipse. 
The missing part gradually gets smaller, and after a few hours,
it's all over, and we have the full Sun back.

There's a lot more to say about each of these. But you know, quite
frankly, I feel like I've given you 10 points' worth.  I hope you agree.

Pretty sure the answer is b : )