I have a Carrier HVAC heating and cooling system in my home and the Honeywell 3 zone board went out. I called a HVAC company and they state that I need to replace the Honeywell 3 zone board, transformer and damper for $800. Is this a reasonable price?

May depend on where you live. Parts on Ebay run about $350 so that would be low end. Add service call and hourly rate and $800 doesn't appear that far off. Call a couple of other HVAC companies.

Call 2 or 3 more contractors. Then you can have a broader baseline to compare prices.