Two common wires

I’m replacing a Hunter X-Core with 4 zones. The Hunter controller has two green wires to Common (see attached) – should both of those wires go to Common in my Rachio 3?

I would say very likely. I see a red wire going to P which is either a pump or master valve and the first zone is also red. If your Rachio has multiple commons, it does not matter which one you connect each of them to and they can be connected to different ones. Remember to configure in the app whether it is a pump or master valve.