how to run 12V x 2 battery inverter in (12V x 2)+(12V x 2)?
The inverter will be happy, but the batteries won't. The new ones will be constantly trying to recharge the old ones and wasting mucho power, maybe ruining your nice new batteries in the process. 
You need to isolate the two battery packs from each other. The simplest way is to incorporate a nice high current diode with each battery pack to allow the electricity to flow out of the batteries only.
You don't mention what you have in the way of a charging system. If the batteries are charged in place as in a UPS, then this will break that charging. A separate charge feed would need to be provided to each battery pack.