Min jakke hænger i garderoben, så jeg tager kun programbladet med ind i salen.

Because jakke is a common-gender noun in Danish: en jakke.

For singular possessives, Danish uses:

• min with en-words
• mit with et-words
• mine with plurals

So:

• en jakke → min jakke
• et hus → mit hus
• mine sko → mine sko

Hænger means hangs / is hanging.

Danish often uses more specific verbs than English in situations like this. Instead of just saying my coat is in the cloakroom, Danish naturally says my coat hangs in the cloakroom, because that is how a coat is typically stored there.

So Min jakke hænger i garderoben sounds very natural.

Garderoben means the cloakroom / the coat check / the wardrobe area, depending on context.

The ending -en is the definite article added to the noun. In Danish, the definite article is usually attached to the end of the noun:

• en garderobe = a cloakroom / wardrobe
• garderoben = the cloakroom

So Danish often says the cloakroom as one word: garderoben.

Because så here means so, as a coordinating conjunction.

In Danish, when så joins two main clauses in the sense of so / therefore, the next clause keeps normal main-clause word order:

• Min jakke hænger i garderoben, så jeg tager ...

That is different from cases where a fronted adverb triggers inversion. Here, så is simply linking two clauses, so jeg stays before tager.

Danish often uses the present tense to talk about something happening now, next, or in the near future, especially when the context makes it clear.

So jeg tager kun programbladet med ind i salen can naturally mean:

• I’m only taking the program with me into the auditorium
• So I’ll only take the program into the auditorium

This is very common in Danish.

Kun means only.

Its position shows what it mainly modifies. In jeg tager kun programbladet med ind i salen, the most natural reading is:

• I am taking only the program leaflet, not other things.

So kun is placed before programbladet to focus on that noun phrase.

Compare:

• Jeg tager kun programbladet med = I’m taking only the program leaflet
• Jeg tager programbladet kun med ind i salen = much less natural, and the focus becomes unclear

Programbladet means the program leaflet / the programme booklet / the playbill, depending on the setting.

It is made from:

• program = program
• blad = sheet / leaflet / paper

Together, programblad means a printed program handout.

The ending -et shows it is a definite singular neuter noun:

• et programblad = a program leaflet
• programbladet = the program leaflet

Because the sentence refers to a specific program leaflet, not just any one.

Danish uses the definite form when the thing is understood from the situation. If you are at a theatre or concert, there is typically a particular program leaflet already being referred to, so programbladet is natural.

Compare:

• Jeg tager et programblad = I’m taking a program leaflet
• Jeg tager programbladet = I’m taking the program leaflet

Because tage ... med means take ... along / take ... with you.

The particle med adds the idea of bringing something along. Without med, tage can just mean take in a more general sense.

So:

• Jeg tager programbladet = I take the program leaflet
• Jeg tager programbladet med = I take the program leaflet with me

In this sentence, med is important because the speaker is bringing it into another place.

Med ind means something like with me in or along inside.

It combines:

• med = along / with
• ind = in, inward

So tage noget med ind means take something along inside.

In the full phrase tager kun programbladet med ind i salen, the idea is:

• I only take the program leaflet with me into the auditorium

This kind of particle combination is very common in Danish:

• gå ind = go in
• tage med ind = take along in
• komme ud = come out
• tage med ud = take along out

Because this expresses movement into the hall/auditorium.

A useful contrast is:

• i salen = in the auditorium (location)
• ind i salen = into the auditorium (movement)

Here the speaker is moving from one place to another, so ind i is natural.

The sentence already has med ind, and then i salen specifies where the movement goes: into the auditorium.

Salen is the definite form of sal, which often means hall, auditorium, or main room, depending on context.

At a theatre, cinema, concert venue, or similar place, salen usually means the room where the audience sits.

So:

• en sal = a hall / auditorium
• salen = the hall / auditorium

Yes, very much so.

Several words point to that kind of setting:

• garderoben = the cloakroom / coat check
• programbladet = the program leaflet / playbill
• salen = the auditorium / hall

So the sentence sounds like something someone would say when arriving at a performance venue and leaving their coat before going in.

It is fairly close to English, but with a few very Danish features:

• definite endings on nouns: garderoben, programbladet, salen
• present tense used for near-future meaning: jeg tager
• verb-particle combinations: tager ... med ind
• specific verb choice: hænger instead of just is

A very literal breakdown would be:

• Min jakke = my coat
• hænger = hangs
• i garderoben = in the cloakroom
• så = so
• jeg tager = I take / I’m taking / I’ll take
• kun programbladet = only the program leaflet
• med ind i salen = with me into the auditorium

So the sentence is close to English in overall structure, but the details are very typically Danish.