Hun går tilbage til kontoret, fordi der mangler et stempel på papiret.

Because the two words do different jobs:

• tilbage = back
• til = to

So gå tilbage til kontoret literally means go back to the office.

If you said går til kontoret, that would just mean goes to the office, without the idea of returning.

Til is used for movement toward a destination.

• Hun går til kontoret = she goes to the office
• Hun er på kontoret = she is at the office

So in this sentence, she is moving toward the office, which is why til is the natural choice.

Because they are definite singular forms of neuter nouns.

• et kontor = an office

• kontoret = the office

• et papir = a paper
• papiret = the paper

In Danish, the definite article is often added to the end of the noun instead of being a separate word like English the.

Because stempel is a neuter noun in Danish, so it takes et in the singular indefinite form:

• et stempel = a stamp
• stemplet = the stamp

You simply have to learn whether a noun is an en-word or an et-word.

Here, der is a kind of dummy subject, similar to English there in sentences like:

• There is a problem
• There is a stamp missing

So der mangler et stempel means something like:

• there is a stamp missing
• a stamp is missing

This der does not mean a physical place like there in over there.

Because mangle means to be missing or to be lacking.

So:

• Der mangler et stempel = a stamp is missing

This is the normal verb for something absent from a document, list, form, etc.

A useful contrast:

• mangle = be missing / not be there
• savne = miss someone or something emotionally, or feel the absence of it

So you would not normally use savne for a missing stamp on a paper.

It can mean both, depending on context.

Danish present tense often covers both:

• she goes
• she is going

So Hun går tilbage til kontoret can naturally mean She goes back to the office or She is going back to the office.

Danish usually does not need a separate form like English is going.

No. In Danish, the present-tense verb form stays the same for all persons.

For example:

• jeg går
• du går
• hun går
• vi går

So går does not change just because the subject is hun.

Because på is the normal preposition for something appearing on the surface of a paper or document.

So:

• et stempel på papiret = a stamp on the paper

If you said i papiret, it would sound more like something physically inside the paper material itself, which is not what is meant here.

Because fordi introduces a subordinate clause.

In Danish, many people write a comma before such clauses:

• Hun går tilbage til kontoret, fordi der mangler et stempel på papiret.

You may also see sentences without that comma, depending on the comma style being used. So the comma here is completely normal.

Because hun is the subject form, and hende is the object form.

In this sentence, she is the one doing the action, so Danish uses hun.

Compare:

• Hun går tilbage til kontoret = She goes back to the office
• Jeg ser hende = I see her