Jeg hænger jakken på den her krog, men tasken på den der krog ved døren.

Because they are in the definite form: jakken = the jacket, tasken = the bag, døren = the door.

In Danish, the definite article is often attached to the end of the noun instead of being a separate word:

• jakke = a jacket

• jakken = the jacket

• taske = a bag

• tasken = the bag

• dør = a door
• døren = the door

This is one of the biggest differences from English.

Because with demonstratives like den her and den der, Danish normally uses the noun in its base form, not the suffixed definite form.

So you say:

• den her krog = this hook
• den der krog = that hook

Not:

• den her krogen
• den der krogen

A useful rule is:

• krogen = the hook
• den her krog = this hook
• den der krog = that hook

So Danish does not stack both kinds of definiteness here.

Because krog is a common-gender noun in Danish, and common-gender nouns take den.

Danish has two grammatical genders:

• common gender → en / den
• neuter → et / det

Since it is:

• en krog

it becomes:

• den her krog
• den der krog

If it were a neuter noun, you would use det instead.

They work much like this and that in English.

• den her krog = this hook, the one near me / the one I’m indicating as close
• den der krog = that hook, the one farther away / more distinct from the first one

Literally, her means here and der means there, but together with den they function as everyday demonstratives:

• den her = this
• den der = that

So the sentence contrasts two different hooks: this one and that one.

Yes. Denne krog also means this hook.

But there is a style difference:

• den her krog is very common in everyday spoken Danish
• denne krog can sound a bit more formal, written, or pointed

Similarly:

• den der krog = that hook
• den krog can sometimes mean that hook depending on context, but it is less directly contrastive

So in natural speech, den her / den der is extremely common.

Because Danish often leaves out repeated words when they are already understood from the first part of the sentence.

The full version would be:

• Jeg hænger jakken på den her krog, men [jeg hænger] tasken på den der krog ved døren.

The second jeg hænger is omitted because it would be repetitive.

This kind of ellipsis is very natural in Danish, just as English can sometimes omit repeated material:

• I’ll take the jacket, and you the bag.

So the second half is understood as:

• but the bag on that hook by the door

with I hang/put understood from the first half.

It is the present tense of hænge, and Danish present tense can cover several meanings that English splits up differently.

Depending on context, jeg hænger ... can mean things like:

• I hang ...
• I am hanging ...
• I’m putting ... up/on ...

In a sentence like this, it usually sounds like a current action or an immediate practical statement about where each item goes.

So Danish present tense is often more flexible than English present tense.

Because in Danish, things are hung on a hook, so på is the natural preposition.

• på en krog = on a hook
• på døren = on the door
• på væggen = on the wall

Here, på marks the place where the jacket and bag are being hung.

This matches English fairly closely in this case: on a hook.

Ved døren means by the door or near the door.

It describes which hook is meant:

• den der krog ved døren = that hook by the door

So ved døren belongs with krog, not with tasken.

In other words, it is not saying the bag is somehow “by the door” separately; it is identifying the specific hook: the hook that is by the door.

Yes. It is very normal.

The structure is:

• Jeg = subject
• hænger = verb
• jakken = object
• på den her krog = place/directional phrase

So it follows a straightforward pattern:

Subject + verb + object + prepositional phrase

That is a completely natural way to say it in Danish.

The only slightly special thing in the full sentence is not the first clause, but the fact that the second clause leaves out the repeated jeg hænger.