Per Tesla: "To ensure reliable operation during power outages, at least one Powerwall is required for each 7.6 kW AC of solar included in the backup circuit." So for the 12 kW system, you'll need a min of two Powerwalls and three Powerwalls for the 16 kW system.
As we talked about on the other thread Tesla's guidance is way too simplistic, IMO. It does not take in to account inverter ratings, panel orientation, local irradiance levels, static and dynamic house draw, usage patterns, etc etc.
To be relevant to this thread I'd add a bullet to the OP saying "don't follow Tesla's 7.6kW AC per Powerwall requirement blindly".