According to the dictionary, aufmachen is used with accusative:
Then why is
Wann macht der Supermarkt auf?
Wann macht den Supermarkt auf?
For example here, but also in some other sites.
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Aufmachen can be used as both, a transitive and an intransitive verb. So there you can aufmachen something but you can also just aufmachen. It is the same for the English verb to open.
Er macht den Laden auf. (acc)
He opens the store.
Der Laden macht um 6 auf.
The store opens at 6.
Wann macht der Supermarkt auf? is written with Supermarkt in the nominative case as indicated by the determinative der.
A simple test as to why this is the case would be to ask:
What (or who) is opening?
Answer: The super market. Nominative case nouns represent subjects of sentences or in vernacular: "the who or what, which is doing the action".
Hypothetically, if you were to write Wann macht den Supermarkt auf?, it would imply a subject (noun or pronoun) just before den Supermarkt:
Wann macht der Verkäufer den Supermarkt auf?
This is supplemental material This does not deal directly with the question, but I am including it because I know that understanding cases can result in headaches. It is rare, but sometimes a reversal of the standard dative-accusative word-order occurs for various reasons (e.g. emphasis, contrast)
This is rare, because it happens in rare situations and this usage may depend on where the language user is from). Example of contrast:
Jimmy: Er hat dem Jungen den Lastkraftwagen geschenkt!
Roger: Nein, Jimmy! Er hat das Auto dem Jungen geschenkt, nicht den Lastkraftwagen!
or with pronouns (this syntax occurs when both objects are pronouns):
Der Chef gibt ihn ihr.
But interestingly sometimes without pronouns:
Der Chef gibt den Brief der Sekretärin.