Sie macht den Briefkasten auf und findet einen Brief.

Breakdown of Sie macht den Briefkasten auf und findet einen Brief.

und
and
finden
to find
sie
she
der Brief
the letter
der Briefkasten
the mailbox
aufmachen
to open
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Questions & Answers about Sie macht den Briefkasten auf und findet einen Brief.

What does aufmachen mean and why is it split into macht … auf here?
aufmachen is a separable-prefix verb meaning “to open.” In a main clause the prefix auf detaches and moves to the end of the clause, while the verb stem (here macht) stays in the verb‑second (V2) position. So Sie macht den Briefkasten auf literally shows macht in second position and auf at the end.
Why is auf at the end of the clause instead of next to machen?
Because auf is not a preposition here but part of the separable verb aufmachen. In main clauses German always splits separable verbs, putting the prefix at the very end. You cannot place it before the noun (e.g. macht auf den Briefkasten would be ungrammatical in German).
What case is den Briefkasten and why is it den?
den Briefkasten is the direct (accusative) object of aufmachen. The noun Briefkasten is masculine, so its definite article der changes to den in the accusative singular.
What case is einen Brief and why is it einen?
einen Brief is also a direct object (accusative) of finden. Brief is masculine, and the masculine indefinite article ein becomes einen in the accusative singular.
Could Sie here mean “you” (formal) instead of “she”?
Although the formal “you” is also Sie, its verb form would be machen (Sie machen). Here the verb is macht, which is 3rd person singular, so Sie clearly means “she.”
Why is the pronoun Sie not repeated before findet?
In German, when two main clauses share the same subject and are joined by und, you typically omit the repeated subject in the second clause. It’s understood that “she” is still the subject of findet.
How does the word order work in this sentence?

The sentence has two coordinate main clauses linked by und. Each clause follows the V2 (verb‑second) rule:
1) Clause 1: Sie (1st position), macht (2nd), den Briefkasten (object), auf (separable prefix at end).
2) Clause 2 (after und): findet (2nd position counting und as connector), einen Brief (object).

Why is Briefkasten written as one word and why is it capitalized?
German combines nouns into a single compound noun: Brief + Kasten = Briefkasten (“mailbox”). All German nouns are capitalized, hence the uppercase B.
Could I use öffnen instead of aufmachen here?

Yes. öffnen (“to open,” more formal) works the same way:
Sie öffnet den Briefkasten und findet einen Brief.
Both sentences are correct; öffnen is just a bit more formal than aufmachen.