In Guns, Germs, and Steel, how did food production lead to Spanish advantages over the Inca?

First of all, please note that both the Spanish and the
Inca had food production.  It was not the existence of food production per se that gave
the Spanish their advantage.  Instead, it was the fact that the Spanish (and Eurasians
in general) had had food production for longer and in more places than the Incas and
other natives of the Americas had.

Eurasia was able to give
rise to many civilizations because it had food production earlier and because food
production could diffuse more easily.  Because of this, the various civilizations could
create technologies and could then trade them with one another.  This allowed them to
benefit from technologies that were devised by other civilizations.  With many
civilizations all creating and adapting technologies, and with them having done so for a
much longer time, the Eurasians had technologies (steel weapons) that the Inca did
not.   One should also note that the longer history of food production meant that the
Eurasians had various infectious diseases that the Inca did
not.

Thus, the fact that Eurasia had food production for
longer led to more civilizations, better technology, and more infectious diseases than
the natives of America had.