“Jeff and me went shopping”

Vs

“Jeff and I went shopping”

If you can take Jeff out and it sounds right then it’s grammatically correct. For example you wouldn’t say “me went shopping”.

“That looks fake to Jeff and me”

“That looks fake to Jeff and I”

In that case you wouldn’t say “that looks fake to I”.

I never understood this until a technical writer I worked with made it so plain one day.

Edit: formatting