Hello I like to install a thermostat to a natural gas furnace.
Old Thermostat wiring:
Honey Well;
g-green
c-blue
r-red
w-white
y-yellow

New Thermostat RTH6350D Honey Well;
w2-y2-g-w not use y-r-rh

I Did what the manual ask me to do, but it did not work. Any ideas?

Take another look normally the instructions are right,, I hope you killed the power to furnace before starting project as its very easy to fry the transformer while changing tstats.