How can I download and install iOS 15.6 on iPhone 6s Plus?

You cannot install iOS 15.6, specifically. As Mr. Timmons says, it is no longer available.

If you have an iPhone 6s Plus, you can install the latest release of iOS 15 – currently iOS 15.8.4. Any app that requires "iOS 15.6 or higher" should work on iOS 15.8.4 (barring unexpected bugs).

About iOS 15 Updates - Apple Support

Update your iPhone or iPad - Apple Support

Updating iOS: common issues and solutions - Apple Community

Note that the 's' in the model name is significant. The iPhone 6 Plus (no "s") cannot update past iOS 12.*.

What do you see at settings - general - software update?

iOS 15.6 is no longer available.

Tap Settings > General > Software Update

What is the message that you see?