Hi Siebe. In case it could help, I’d like to give examples similar to what Lal has given in the past. Lal and anyone, always feel free to correct me if I’m wrong.
Tanha via greed:
You just finished listening to your favorite song. Even though that event has passed, you continue to consciously think about that song, with the thoughts: “that is such a lovely song, I could listen to it over and over again, I might listen to it again in a few minutes.”
Tanha via hatred:
Someone you don’t like just said something mean to you. Even though that event has passed, you continue to consciously think about that person, with the thoughts: “I can’t tolerate that person, how can he say that to me, I need to think of a good comeback and tell him that the next time I see him.”
Those thoughts in the quotes are the upadana step.
I’m not sure about what example to give for moha. Maybe something with micca ditthi? The thoughts: “if I do this particular procedure everyday, then I am guaranteed to get access to heaven forever in the afterlife, therefore I have to do this procedure diligently.”