Why can't the sentence be translated to Norwegian as 'Hun byr ham 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.
Ok, got it!
why is a sentence here in this course "jeg byr deg huset mitt"?
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.
good to know that "pa" is needed when "by" comes together with food.