Apple Support says my Series 6 watch will pair with my iPhone 6s but no go. How to fix?

Sorry, if your Apple Watch Series 6 uses watchOS 10, you won't be able to pair it on an iPhone using iOS 15.8.2. For watchOS 10, the iPhone needs to use iOS 17, which unfortunately is not compatible with your iPhone.

I agree, what Apple implies is you can use it with that phone:

Apple Watch Series 6 - Technical Specifications - Apple Support

"Apple Watch Series 6 require an iPhone 6s or later with iOS 14 or later."

If you're within the time period you could see about getting a refund.

Click here to read about Apple Store Returns & Refunds--> Returns & Refunds - Shopping Help - Apple - For the USA "You have 14 calendar days to return an item from the date you received it." The return terms may be different in some countries (the link I provide should open to a page for the country to which your account is set).

- "You can always return the item to any U.S. Apple Store. An Apple Specialist will assist you with your return. Your refund will be processed at that time"

By the way, Apple appears to just presume everybody is only ever running the newest software on their devices and you have already gotten rid of any device that is incapable of doing that. You have to be very careful if you are operating outside those parameters. :-( Our household uses Apple equipment spanning a decade and one of my main jobs is making sure that anything we buy or upgrade results in minimal issues like the one you are experiencing.

I believe (but I’m not absolutely sure) that an Apple Store could install an older version of watchOS that would be compatible with your iPhone if you explain your predicament.