"She is offering him coffee."
Translation:Hun byr ham på kaffe.
The verb is "å by på" when offering food, so you can't omit 'på' in this case.
You can say "Hun tilbyr ham kaffe." however.
I've changed my explanation slightly, seems I can't always be right. "by" is a tricky verb, however, so I'm not entirely sure when you can drop 'på'. It might best be learnt by heart.
ok, thanks good to know that "pa" is needed when "by" comes together with food.