Der hænger et stort skilt over døren ved indgangen.

Here der does not mean there in the usual location sense. It is the existential der, used in sentences like there is / there are in English.

So Der hænger et stort skilt ... is structured a lot like:

• There is a big sign hanging ...

In Danish, this kind of der is very common when introducing something that exists or is located somewhere.

Hænger means hangs / is hanging. Danish often prefers a verb that describes the object’s position or state more precisely.

So:

• Der er et stort skilt over døren = There is a big sign over the door.
• Der hænger et stort skilt over døren = There is a big sign hanging over the door.

The second version is more vivid and more natural if the object is physically suspended or mounted in a hanging position.

Because skilt is a neuter noun in Danish.

Danish nouns are mainly either:

• common gender: take en
• neuter gender: take et

The noun is:

• et skilt = a sign

Because it is neuter, the adjective must agree with it:

• et stort skilt = a big sign

Compare:

• en stor dør = a big door
• et stort skilt = a big sign

So the -t on stort matches the neuter noun skilt.

This is adjective agreement.

The basic adjective is:

• stor = big

But before a singular neuter noun, it usually takes -t:

• et stort skilt

A quick comparison:

• en stor bil = a big car
• et stort skilt = a big sign
• store skilte = big signs

So stort is simply the neuter singular form of stor.

Døren means the door.

In Danish, definiteness is often shown by adding an ending to the noun:

• en dør = a door
• døren = the door

So over døren means over the door.

This is one of the biggest differences from English: Danish often puts the at the end of the noun instead of using a separate word.

Ved usually means by, near, at.

Indgangen means the entrance:

• en indgang = an entrance
• indgangen = the entrance

So ved indgangen means:

• by the entrance
• at the entrance
• near the entrance

In the full sentence, it tells you which door we are talking about, or where the sign is located more specifically.

In practice, it most naturally helps identify the location of the door/sign area: the door by the entrance or over the door at the entrance.

So the sentence is understood as something like:

• There is a big sign hanging over the door by the entrance.

Danish often allows this kind of location phrase without making the relationship overly explicit. Native speakers understand it from context.

This is normal Danish sentence structure for an existential sentence.

The pattern is roughly:

• Der + verb + noun phrase + location

So:

• Der hænger et stort skilt over døren ved indgangen.

This is similar to English:

• There hangs a big sign ...
• more naturally: There is a big sign hanging ...

You could say Et stort skilt hænger over døren ved indgangen, but that sounds more like you are focusing directly on the sign itself, not introducing it as new information.

Yes. That would also be correct.

The difference is:

• Der er ... = neutral existence/location
• Der hænger ... = more specific; it tells you the sign is in a hanging position

So both are possible, but hænger is more descriptive and often more natural for objects like signs, lamps, pictures, coats, etc.

Because Danish usually wants a full, natural noun phrase here, and ved indgangen means by the entrance.

The indefinite form would be:

• en indgang = an entrance

The definite form is:

• indgangen = the entrance

In a real situation, speakers often mean a specific entrance that both speaker and listener can identify, so the definite form is natural.

The infinitive is:

• at hænge = to hang

The present tense is:

• hænger = hangs / is hanging

So in this sentence, hænger is present tense.

A few forms:

• at hænge = to hang
• hænger = hangs / is hanging
• hang = hung
• har hængt = has/have hung

Usually, yes. Over døren means over the door.

It can refer to position higher than something, often directly above it.

In this sentence, it means the sign is positioned above the door.

So over works very much like English here.

A rough learner-friendly pronunciation could be:

• Dair HENG-er ed STORD sgeld O-ver DUR-en veð IND-gang-en

A few notes:

• der is often pronounced something like dair
• hænger has a vowel that does not exist exactly in English; it is a front vowel, somewhat like the vowel in man, but tenser
• døren has ø, which is also tricky for English speakers
• skilt is pronounced with a short i and a clear final t

You do not need perfect pronunciation at first; the most important thing is to notice the rhythm:

• Der HÆNger et STORT skilt OVer DØren ved INDgangen

The most useful things to notice are:

1. Existential der

   • Der hænger ... = There is/are ... hanging

2. Noun gender

   • et skilt

3. Adjective agreement

   • et stort skilt

4. Definite endings

   • døren = the door
   • indgangen = the entrance

5. Natural location phrase

   • over døren ved indgangen

If you understand those five points, you understand most of the grammar of the sentence.