I have an iPhone XR running iOS 16.5.1- I am trying to download and install 16.6 but phone does not recognize my wifi even though I have excellent connection the the internet and wifi works on all at her sites.

See the following Apple articles:

Connect to Wi-Fi on your iPhone, iPad, or iPod touch

Connect to Wi-Fi on your iPhone, iPad, or iPod touch - Apple Support

If your iPhone, iPad, or iPod touch won’t connect to a Wi-Fi network

If your iPhone or iPad won't connect to a Wi-Fi network - Apple Support

Check the route settings -> Recommended settings for Wi-Fi routers and access points

Recommended settings for Wi-Fi routers and access points - Apple Support

If you need help with your Wi‑Fi password

If you need help with your Wi‑Fi password – Apple Support (UK)

•  You need to sign in to your router.
• The Wi-Fi network name, or SSID (service set identifier), is the name your network that has a password.

or If you have iOS 16 / iPadOS 16:

Go to -> Settings -> tap Wi-Fi -> tap on the hideen Password -> enter Passcode -> you will then see the Wi-Fi Password.

If they are On, turn Off Hotspot & VPN.

Any chance you have a VPN installed on your iPhone? If you do, at a minimum, turn it off and try to update. Even better would be to remove the VPN as they can cause issues like this and more and aren't needed on iPhone at all.