For starting a 16k BTU air conditioner with a Honda 2000, you will want to use what is called a "Soft Start" device. It's an electrical module that you wire between the generator's output and the air conditioner's input. Think of it as a valve that opens slowly to control the amount of current it allows to the air conditioner while the compressor is starting to turn.
When you start an electrical load, such as a motor, the starting current shoots up pretty high and then gradually ramps down to the full load current that the device requires to run. This is called "in-rush" current. As people above have already mentioned, the electrical name plate on your air conditioner lists how many Amps it draws. That is the current draw when it is up and running. The Amps will be a lot higher as it starts up.
What a Soft Start does is choke that startup current down and stretch it over a longer period of time, such that the inrush current is kept to a controllable level. The device will take a little longer to get up to full current, meaning the motor will turn a little slowly at first.
The ramp up time is rather quick- it's not really that noticeable. We are talking a few seconds here. But a Soft Start will keep you from tripping breakers or knocking the generator off line when you start the air conditioner.
A Soft Start is sized based on the voltage and rated current of the load device (your air conditioner) that will be connected to it.
Here's an example of a soft start: (you want a "single phase" unit)
Single Phase HVAC Compressor Soft Start
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