Can I connect a newly bought Apple Watch series 3 to my iPhone 6?

A new bought Apple Watch will have watchOS 6 preinstalled, so your phone has to be running iOS 13.

But, Apple Support might be able to downgrade your watchOS, if you contact them and explain your situation.

If the watch has software version watchos6 then it will NOT pair with an iphone 6,watchos6 requires an iphone with ios13 or higher an iphone 6 will only update to ios12,for ios13 you need an iphone 6s or higher.If the watch has watchos5 or below then it WILL pair.

You're welcome 🙂