Does Multani, Yavimaya's Avatar die to Fall of the Thran?
Multani does not die to Fall of the Thran, or any other mass land destruction effect, for two different reasons.

First, there is no such thing as being "between zones". When lands get destroyed, they go directly from the battlefield to the graveyard. So, there is never a time when Multani is a 0/0.

Second, dying due to having 0 toughness is a state based action, and those are never checked in the middle of a spell or ability resolving. So even if a similar effect caused Multani to briefly be a 0/0 in the middle of resolution, Multani would stay alive if it has more than 0 toughness after the effect is done resolving.