Learn Hardcore Danish: Kunstneren hænger sine nye malerier i galleriets store sal. - The artist hangs his new paintings in the gallery’s large hall.

Kunstneren is the subject.
The paintings belong to that same subject.
Therefore you must use sine (reflexive, plural) and not hans or hendes.

If you said:

Kunstneren hænger hans nye malerier …

it would normally mean The artist is hanging his (someone else’s) new paintings…, i.e. the paintings belong to some other man, not the artist himself.

So sine here means his/her own and clearly refers back to kunstneren.

Why is it sine and not sin or sit?

The choice between sin, sit, and sine depends on the thing owned, not on the owner.

sin – singular, common gender: sin bil (his/her own car; bil is common gender)
sit – singular, neuter gender: sit hus (his/her own house; hus is neuter)
sine – plural (both genders): sine malerier (his/her own paintings)

Since malerier is plural, you must use sine.

What exactly does hænger mean here – hangs or is hanging?

Danish does not have a separate continuous form like English is hanging. The simple present hænger can cover both:

a general action: The artist hangs his new paintings (whenever he has an exhibition).
an action happening now: The artist is hanging his new paintings (right now).

Context decides which English translation fits better. Grammatically, both hangs and is hanging are possible translations of hænger here.

Is hænger transitive or intransitive in this sentence?

Here hænger is transitive because it has a direct object:

Verb: hænger
Direct object: sine nye malerier

So the meaning is The artist is hanging (something), not The paintings are hanging by themselves.

For comparison:

Malerierne hænger i galleriets store sal.
(The paintings are hanging in the gallery’s large hall.) – intransitive

Could/should we say hænger … op instead of just hænger?

You often hear hænge noget op for the action of putting something up so that it hangs.

Kunstneren hænger sine nye malerier op i galleriets store sal.

This is very natural Danish and clearly focuses on the action of putting the paintings on the walls.

Using just hænger is also grammatically correct, but in everyday speech, hænge op is often preferred for this concrete action. Without op, hænger can sound a bit more neutral or even slightly closer to a description of state, depending on context.

How do we form galleriets from galleri?

Galleriets is the genitive (possessive) form of galleriet.

Steps:

Base noun (indefinite neuter): et galleri
Definite form: galleriet (the gallery)
Genitive: add -s to the definite form: galleriets (the gallery’s)

This follows the general pattern:

huset → husets (the house → the house’s)
skolen → skolens (the school → the school’s)
galleriet → galleriets (the gallery → the gallery’s)

Why is it store sal and not stor sal?

The adjective stor becomes store here because the noun phrase is definite due to the genitive galleriets.

Compare:

en stor sal – a large hall (indefinite, no genitive/possessive)
den store sal – the large hall (definite)
galleriets store sal – the gallery’s large hall (also definite)

In Danish, when a noun is made definite by a genitive (like galleriets) or by a possessive pronoun (like min, din), the adjective takes the -e ending (the “weak” form):

mit store hus – my big house
galleriets store sal – the gallery’s big hall

So galleriets stor sal would be ungrammatical.

Why is there no den before store sal, like i galleriets den store sal?

In Danish you normally do not combine:

a genitive (like galleriets)
with
a separate definite determiner (den, det, de) or a definite ending on the noun at the same time.

You choose one way of making it definite:

den store sal i galleriet – the large hall in the gallery
(definite with den
- adjective ending -e
  - bare noun)
galleriets store sal – the gallery’s large hall
(definite through the genitive galleriets, adjective ending -e, bare noun)

So i galleriets den store sal sounds wrong in standard Danish.

Why is the preposition i used and not på?

For rooms and enclosed spaces, Danish generally uses i:

i stuen – in the living room
i salen – in the hall
i galleriets store sal – in the gallery’s large hall

På is used more for surfaces, islands, institutions, etc.:

på bordet – on the table
på øen – on the island
på skolen – at the school (institution, not physically inside a specific room)

So i galleriets store sal is the natural choice. På galleriets store sal would only make sense in a very special meaning, like being on top of the roof of the hall.

Can we change the word order, for example: I galleriets store sal hænger kunstneren sine nye malerier?

Yes, that is correct Danish and quite natural.

Danish is a verb‑second language in main clauses. The finite verb (hænger) must be in second position, but what comes first can vary:

Neutral order: Kunstneren hænger sine nye malerier i galleriets store sal.
With fronted place phrase: I galleriets store sal hænger kunstneren sine nye malerier.

In the second version, you put extra emphasis on the location (it is in that hall that this happens), but the basic meaning is the same.

Why is it malerier and not malerierne?

Malerier is the indefinite plural (paintings), while malerierne is the definite plural (the paintings).

sine nye malerier – his/her own new paintings (being introduced or mentioned for the first time)
sine nye malerierne – incorrect; you cannot combine sine with a definite ending here

If the paintings were already known in the context and you wanted to say the new paintings, you could rephrase, for example:

Kunstneren hænger de nye malerier i galleriets store sal.
(The artist is hanging the new paintings …)

What is the difference between kunstneren and en kunstner?

en kunstner – an artist, non‑specific, you are mentioning some artist for the first time.
kunstneren – the artist, specific, the speaker assumes the listener knows which artist is meant (from context, earlier in the text, etc.).

Danish normally marks definiteness with an ending on the noun:

kunstner – artist
kunstneren – the artist

Why is the adjective ny in the form nye here?

Two reasons lead to nye:

Plural:
Malerier is plural, and in plural adjectives always take -e:
- et nyt maleri – a new painting (singular, neuter)
- nye malerier – new paintings (plural)
Possessive before the noun:
When you have a possessive pronoun (sin/sit/sine, min, din, etc.) before the noun, adjectives also take -e:
- mit nye maleri – my new painting
- mine nye malerier – my new paintings
- sine nye malerier – his/her own new paintings

So nye is required here; sine ny malerier would be incorrect.