The new iOS 16 is not showing up in my Software Update. How do I download this?

Have you previously used a beta version on your iPhone? If so, remove the beta profile, restart the phone and check again for the update.

How to uninstall iOS or iPadOS beta software - Apple Support

You have not told us what model phone you want to update, so we can't offer much help. If it is an older model, it may not be eligible for the upgrade.

You are welcome.