How do I update iTunes on my 10.10.5 macbook pro to sync with my iPhone 8+ ?

For iOS 13 or later you need iTunes 12.8.2.3 or better running on OS X 10.11.4 or better. See How to upgrade to OS X El Capitan - Apple Support if required.

Assuming a suitable version of iTunes is in place but your device still won't connect then in Finder use the menu item Go > Go to Folder..., copy the following text, paste it into the dialog box and press enter:

/System/Library/PrivateFrameworks/MobileDevice.framework/Versions/Current/Resources

Unlock your device and connect it to USB. Double click on MobileDeviceUpdater in the folder that has opened. It should notify you of a software update. Install it and iTunes should hopefully recognize your device.

tt2

Hello Dw888 and welcome to Apple Support Communities.

I see you're trying to get a MacBook Pro running Yosemite to sync with an iPhone 8 Plus.

How to upgrade to macOS High Sierra - Apple Support

In order to get a version of iTunes that will talk to that iPhone running iOS 13, you'll need to update to at least High Sierra.

Cheers.