I am unable to install the iOS 15.8.2 update on my iPhone 6s

Try going onto storage settings then find the iOS update if you downloaded it and delete it. Then restart your iPhone and try again. If this fails:

If you have a Mac with macOS 10.15 or later, Update software on your iPhone, iPad or iPod touch – Apple Support (UK)

If you have a Mac with macOS 10.14 Mojave or earlier or a Windows PC, Update your iPhone, iPad or iPod touch with iTunes – Apple Support (UK)

Else: take your iPhone to an Apple Store and they will do it for free Genius Bar Reservation and Apple Support Options - Apple (UK)

If there's not enough space to update

If there isn't enough space to download and install an update, the software on your device will try to make space. It will remove only app data that it can download again and doesn't remove or relocate any of your data. If your device still doesn't have enough space, you can use your computer to update your device.

If you can't connect your device to your computer, you can make room for the update by removing content and apps on your device that you don't use. Go to Settings > General > [Device name] Storage.

Learn more about the space your apps and content use.