The number of panels you use depends on the size of your battery, it's voltage, and the relative positioning of your panels. Different kinds of batteries are charged at different rates, typically 1/8C for lead-acid, 1/5C for AGM, or 1/4C for Li. C is the 20hour amphour capacity of your battery.
The maximal charging amperage usually occurs at about 13V for a 12V battery, 26V for a 24V battery, and 52V for a 48V battery. That's not going to be the maximal voltage the battery will see, but the voltage when the battery is charging at about maximal current.
In addition, you usually put in a fudge factor for system losses. For panels pointed directly at the sun, the FF might be 0.85X. For panels mounted flat, with lower output, the FF might be 0.6X.
So, for example, here is the panels needed for charging eight 6V 225Ah lead-acid batteries wired in series for a 48V bank.
[225Ah X 1/8C (0.125) X 52V charging] / 0.85 = 1462/.85 =1720W of panels
So, your question can't be answered until YOU specify what type and how big the batteries you have are at your system voltage.
The second question you should be asking is whether or not your battery bank is large enough to support the running of this air-conditioner. It will improve things a lot if you can specify how many watts the unit consumes while running.
In general, the wires from the panel strings first enter a combiner box, then the output of the combiner goes to the controller, then the output of the controller goes to the batteries, and the batteries go to the inverter powering the air-con. Wire gauges changes at each step depending on how much current they are carrying.