Welcome to JOF
I run my 13,500 BTU A/C with a 2400W Yamaha, so taking an educated guess I would say that a 2000W Honda would run a 8,000 BTU A/C. I believe this was confirmed in another JOF thread recently, but I was unable to locate it.
Hopefully some members will chime in and confirm my statement.
Bob
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2016 GM 2500HD 6.0L/4.10
2018 Jay Flight 24RBS
2002 GM 2500HD 6.0L/4:10 (retired)
2005 Jayco Eagle 278FBS (retired)
1999 Jayco Eagle 246FB (retired)
Reese HP Dual Cam (Strait-Line)