Die Benutzernummer steht auf der Ausleihquittung.

Because Nummer is a feminine noun in German: die Nummer.

Benutzernummer is a compound noun:

• Benutzer = user
• Nummer = number

In German, the last part of a compound noun determines the gender. Since Nummer is feminine, the whole word is feminine too:

• die Nummer
• die Benutzernummer

That is why the sentence begins with Die Benutzernummer.

Benutzernummer literally means user number.

In context, it usually means something like:

• a user ID
• a membership number
• a library user number
• an account number assigned to a person using a service

Since the sentence also contains Ausleihquittung (a borrowing/check-out receipt), this is very likely a library context, so Benutzernummer probably means the library user's ID number.

Ausleihquittung is another compound noun.

It is made from:

• Ausleihe / ausleihen = loan / to borrow, to check out
• Quittung = receipt

So Ausleihquittung means something like:

• borrowing receipt
• check-out receipt
• loan receipt

As with most German compounds, the meaning is usually understood from the parts, and the final element determines the gender:

• die Quittung
• therefore die Ausleihquittung

That is why the sentence says auf der Ausleihquittung.

Yes, stehen literally means to stand, but in German it is also commonly used for written information appearing somewhere.

So Die Benutzernummer steht auf der Ausleihquittung means:

• the user number is written on the receipt
• the user number appears on the receipt

This is very natural German.

Similar examples:

• Die Adresse steht auf dem Formular. = The address is on the form.
• Der Preis steht auf dem Etikett. = The price is on the label.

English often uses is or appears, but German often uses steht in this kind of context.

German usually uses auf for information shown on a surface, including paper, forms, signs, labels, and receipts.

So:

• auf der Quittung = on the receipt
• auf dem Formular = on the form
• auf dem Schild = on the sign

Using in would suggest something more like inside the content of a text or document, which is not the normal choice here.

So auf der Ausleihquittung is the natural way to say on the receipt.

Because auf is a two-way preposition. That means it can take either:

• accusative for direction/movement
• dative for location

Here, the sentence describes a location: the number is located on the receipt. There is no movement.

So we use dative:

• die Ausleihquittung → nominative
• der Ausleihquittung → dative

Compare:

• Die Benutzernummer steht auf der Ausleihquittung.
  The user number is on the receipt. → location → dative
• Ich schreibe die Nummer auf die Quittung.
  I write the number onto the receipt. → direction/placement → accusative

The sentence follows the normal German main-clause pattern:

Die Benutzernummer | steht | auf der Ausleihquittung
subject | verb | prepositional phrase

So:

• Die Benutzernummer = subject
• steht = verb
• auf der Ausleihquittung = where it is

This is very straightforward German word order: subject + verb + other information.

Yes, absolutely.

German allows different elements to come first, as long as the finite verb stays in second position in a main clause.

So both are correct:

• Die Benutzernummer steht auf der Ausleihquittung.
• Auf der Ausleihquittung steht die Benutzernummer.

The difference is mainly emphasis:

• starting with Die Benutzernummer focuses first on the number
• starting with Auf der Ausleihquittung focuses first on the location

Both are natural.

German often uses the definite article where English might prefer a possessive like your.

So depending on context, Die Benutzernummer steht auf der Ausleihquittung may naturally be understood as:

• The user number is on the receipt
• or, in practical context, Your user number is on the receipt

German does not always need to say Ihre Benutzernummer unless it is important to make possession explicit.

So the definite article die is normal here.

In a neutral reading, the sentence simply gives information:

Die Benutzernummer steht auf der Ausleihquittung.

If spoken naturally, the stress often falls near the end, especially on the new information:

• ... auf der Ausleihquittung

But if someone is contrasting things, the stress could shift:

• Die Benutzernummer steht auf der Ausleihquittung.
  (not something else)
• Die Benutzernummer steht auf der Ausleihquittung.
  (not somewhere else)

So the grammar stays the same, but spoken emphasis can change what feels most important.

Yes. German very often creates nouns by combining smaller nouns into one larger compound noun.

Examples similar to this:

• Telefonnummer = telephone number
• Kundennummer = customer number
• Mitgliedsnummer = membership number
• Benutzername = username
• Ausleihfrist = borrowing period

This is one of the most important patterns in German vocabulary. When you see a long word, it often helps to split it into parts:

• Benutzer + Nummer
• Ausleih + Quittung

That makes long words much easier to understand.