I'm turning my deck into a combination deck-patio. That is, half of
the deck will be converted to stamped cement patio and the other half
will be constructed of a wood composite (e.g. Trex). This design was
selected because the house is on a hill and the area where the
deck/patio will be slants away from the house. My question is, for a
cement application like this, how can the gravel/sand/earth foundation
for the cement be held in place where the patio meets with the wood
deck? The challenge is that the deck requires 12-20 inches of
clearance below for supporting joists and beams. Since the concrete is
only 4-6 inches thick, over time the sand/gravel/earth below the edge
of the concrete will slowly erode away and the edge of the cement is
likely to settle/fall causing a large crack in my pation. Can you
advise?

Drive up into the hills with a pair of binoculars. Find someone with a
patio like what you want.  Ask them how they did it.  :)

how about driving a thin (but sturdy and weatherproofed) sheet of
metal (the length of the concrete, and the heighth of the concrete
plus a few feet to anchor it below ground) into the ground at the edge
of the cement (provide the cement embankment with a metal edge). if
driving the sheet into the ground is too difficult, have someone weld
spikes or sharp triangular edges onto the bottom of the metal to help
you place it in the ground. without somehow bordering your cement,
you're going to have problems no matter what because cement slowly
continues to expand over time.