بفهم isn't standard Arabic. Usually used: 1) with languages, and things you know. Ex: أنا بفهم عربي I understand Arabic أنا بفهم في الكمبيوتر It means that you can use computer well. 2) When saying that you're not stupid (or stupid, if negative is used) Ex: A: أنت مبتفهمش = أنت غبي You don't understand (=You're stupid) B: أنا بفهم I understand (=I'm not stupid) *All the above is Egyptian dialect. فاهم is standard Arabic and used in dialect too. أنا فاهم الدرس I understand the lesson. *Can be used in standard Arabic and Egyptian. In my opinion, I think it's better to specify which one you're learning, standard or colloquial. Hope this helps.

بفهم = I understand فاهم = I realized ^o^

بفهم= verb فاهم= adjective