"Fall has begun."
Translation:De herfst is begonnen.
But that's precisely what you need to study, because once you start using the language in the real world, there won't be any hints to help you.
• The Present Perfect of intransitive verbs that imply a change of situation/state of the Subject is formed using a form of zijn.
• The Present Perfect of verbs of motion is normally formed using zijn, mostly when referring to the direction of the movement or the change of state/place. If used in another way, then the Present Perfect is formed with hebben.
• The Present Perfect of verbs that are:
√ impersonal (those that only take het as a Subject, like verbs that are used to talk about the weather, such as regenen or sneeuwen),
√ intransitive without implying a change of situation/state of the Subject of the sentence,
is formed using a form of hebben.
• Some verbs are both transitive and intransitive, so you have to follow the rule that was described above (in short: if the verb is used transitively, hebben; if it's used intransitively and there's no change implied, zijn).
Hope this helps.
"Herfst is begonnen" should also be accepted. You don't have to add "de" before the names of the seasons
It is a bit complicated, since some verbs can have both but will have a different meaning. What you need to know is that reflexive verbs always take 'hebben' as auxiliary. Here is a list with the most common verbs that take 'zijn' as an auxiliary. Intransive verbs:aankomen, bevriezen, gaan ('zich verplaatsen'), groeien, komen, ontsnappen, opstaan, rijzen, schrikken, sterven, stijgen, stikken, vallen, verdorren, vergrijzen, verouderen, verschijnen, verstommen, vertrekken, vluchten en worden. Blijken, blijven, gebeuren, geschieden, (ge)lukken, mislukken, slagen, voorvallen en zijn.