How can I connect my Apple Watch Series 6 to iPhone X?

As mentioned before, if your watch has already watchOS 11 installed, it needs an iPhone that is running iOS 18.

Some users managed to get the watchOS downgraded by the official Apple Support and could pair it after that to the older iPhone.

Why won't my Apple Watch SE pair with my … - Apple Community

However, I would recommend buying a newer iPhone instead.

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Your Apple Watch and iPhone must meet the following minimum requirements:

• Apple Watch SE (2nd generation), Apple Watch Series 6 or later, Apple Watch Ultra, or Apple Watch Ultra 2 with watchOS 11 or later
• iPhone XS or later with iOS 18 or later

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copied from: Set up and pair your Apple Watch with iPhone - Apple Support

Have you tried this:

Set up your Apple Watch - Apple Support

If so, on what step does it fail?

That is because to setup and use Apple Watch, it requires an iPhone XR or later on iOS 18 or later. Your iPhone X does not support that and as a result, you would need to buy a newer iPhone to pair them.