How do I update my Apple Watch 4 to watchOS 6 with an iPhone 6?

I am having trouble updating my Apple Watch Series 4 to watchOS 6, as it is saying "update your phone first". The problem is that I cannot update my iPhone 6 to iOS 13, so does that mean I won't be able to update my watch until I buy a newer version of iPhone?

The message you're getting is the same message all users will get until they upgrade their paired iPhones to iOS 13. In other words, you're not just getting this because your iPhone isn't capable of running iOS 13.

Unfortunately, if you're really wanting to take advantage of any of the new features in watchOS 6, you'll need to pair it to an iPhone running iOS 13 before you can upgrade watchOS. And, in your case, this means upgrading your iPhone too.