How can I update my phone to the latest version?

Your 6S can updated as far as 15.7.1

See Update your iPhone or iPad - Apple Support

and follow the instructions to upgrade from an earlier version of iOS or to update from an earlier iteration of iOS 15.

You will see the upgrade invitation at the foot of the screen - as Apple shows in the linked document:

See the articles below.

Update your iOS device.  -

Get help with over-the-air iOS updates  -

Update – Can’t or can’t restore   -

Have you tried using iTunes on a computer or Finder if running Catalina or later to do the update?

Update software on iOS devices in iTunes on Mac. -

Phone, iPad, or iPod touch - Update with Finder.  *

iPhone, iPad, or iPod touch - Update with iTunes.  *

If you see an error when you update or restore your iPhone, iPad, or iPod    *

Updating iOS: common issues and solutions.  -

Update your iPhone or iPad - Apple Support

An iPhone 6s isn't capable of 16 or above. To install 15.7.1, use a computer or the Software Update function in Settings.

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How can I get my iPhone 6s update to new version iOS 15.7.1