Warum steht die falsche Steuerklasse auf der Gehaltsabrechnung?

Because German keeps the finite verb in second position in main clauses, including wh-questions.

So the structure is:

Warum + steht + rest of the sentence

That is different from English, where we usually use does:

Why does the wrong tax class appear on the payslip?

German does not need an extra helping verb like does here.

The subject is die falsche Steuerklasse.

You can tell because:

• it is in the nominative
• the verb steht is singular, matching Steuerklasse

So the basic statement version would be:

Die falsche Steuerklasse steht auf der Gehaltsabrechnung.
= The wrong tax class appears on the payslip.

Because Steuerklasse is a feminine noun in German.

Its dictionary form is:

• die Steuerklasse

So in the sentence you get:

• die falsche Steuerklasse

The article die shows feminine singular nominative here.

Because adjectives placed before a noun usually need an ending in German.

Here, falsch becomes falsche because it comes after the definite article die and describes Steuerklasse.

So:

• die falsche Steuerklasse = the wrong tax class

Compare:

• Die Steuerklasse ist falsch.
  Here falsch comes after the verb, so it has no ending.

This is a very common difference in German:

• attributive adjective before a noun: ending needed
• predicative adjective after sein, werden, etc.: no ending

Because auf is a two-way preposition.

With two-way prepositions:

• dative is used for location
• accusative is used for movement toward a destination

Here the sentence describes a location: the tax class is on the payslip, not moving onto it.

So German uses the dative:

• auf der Gehaltsabrechnung

Since Gehaltsabrechnung is feminine:

• nominative: die Gehaltsabrechnung
• dative: der Gehaltsabrechnung

In German, stehen is often used when written information is shown, printed, listed, or written somewhere.

So:

• Was steht auf der Rechnung? = What is written on the bill?
• Auf dem Formular steht mein Name falsch. = My name is written incorrectly on the form.

In this sentence, steht means something like:

• appears
• is listed
• is shown
• is printed

Using ist would sound less idiomatic here if you mean what information the payslip contains.

German often uses auf with documents, sheets, forms, bills, or screens when talking about information that appears on them.

So:

• auf der Rechnung
• auf dem Formular
• auf dem Bildschirm
• auf der Gehaltsabrechnung

This matches the English idea of something being on a document.

You may sometimes hear in der Abrechnung in other contexts, but auf der Gehaltsabrechnung is very natural when talking about what is printed or listed on the payslip.

It is a compound noun, which is very common in German.

It is made from:

• Gehalt = salary
• Abrechnung = statement, settlement, accounting, pay statement

So Gehaltsabrechnung means something like:

• salary statement
• payslip
• pay statement

In everyday English, payslip is usually the most natural translation.

Also, in German, the last part of a compound usually determines the gender and the basic category of the word. Since Abrechnung is feminine, Gehaltsabrechnung is also feminine:

• die Abrechnung
• die Gehaltsabrechnung

Yes.

It is made from:

• Steuer = tax
• Klasse = class/category

So Steuerklasse literally means tax class or tax bracket/category.

Again, the last part decides the gender:

• die Klasse
• therefore die Steuerklasse

Yes, often it would.

Both words can refer to a pay statement or payslip:

• Gehaltsabrechnung is often associated with salary
• Lohnabrechnung is often associated with wages/payroll

In everyday use, there is a lot of overlap, and both may be understood depending on context. Gehaltsabrechnung is very natural if the person is a salaried employee.

The statement version would be:

Die falsche Steuerklasse steht auf der Gehaltsabrechnung.

That follows normal German main-clause order:

subject + verb + other elements

When you turn it into a wh-question, Warum takes the first position, and the finite verb stays in second position:

• Die falsche Steuerklasse steht auf der Gehaltsabrechnung.
• Warum steht die falsche Steuerklasse auf der Gehaltsabrechnung?

Yes. Depending on context, it could be rendered as:

• Why is the wrong tax class on the payslip?
• Why does the wrong tax class appear on the payslip?
• Why is the wrong tax class listed on the payslip?
• Why is the wrong tax bracket shown on the pay statement?

The German wording is flexible enough to allow several natural English versions. The main grammar point is that steht ... auf often means is written/listed/shown on rather than literally stands on.