Although not really correct, what you said means closer to "this part is mine" rather than "this is my part", so it might be different from what Duolingo tries to say here. Anyway, "bagian ini milik saya" would be more correct. But if you speak like that to natives, they would definitely understand you, and it's not totally wrong because even native speakers sometimes say it that way in daily conversation. But it's not really correct grammatically. In English, you would say "this part" but in Indonesian, it's the other way around, you say "bagian ini". Just like "beautiful girl" means "gadis cantik", in Indonesian the adjective generally comes after the object.