I omklædningsrummet hænger hendes jakke ved brusekabinen.

No. It is the Danish preposition i, meaning in. It is capitalized only because it is the first word of the sentence.

So:

• i = in
• I omklædningsrummet = In the changing room

Danish does not capitalize all nouns the way German does.

Because Danish, like English, makes a lot of compound nouns, but Danish usually writes them as one word.

omklædningsrummet can be broken down like this:

• omklædning = changing clothes / getting changed
• rum = room
• -et = the for a neuter noun in the singular

So:

• et omklædningsrum = a changing room
• omklædningsrummet = the changing room

English often writes similar ideas as two words, but Danish usually joins them.

This is a very common Danish word-order pattern. Danish follows the V2 rule in main clauses: the finite verb usually comes in second position.

Here, the sentence starts with the place expression:

• I omklædningsrummet = first element

That means the verb must come next:

• hænger = second element

Then the subject comes after the verb:

• hendes jakke

So the structure is:

• I omklædningsrummet
  • hænger
    • hendes jakke
      • ved brusekabinen

In English, this sounds a bit literary if translated word-for-word, but in Danish it is completely normal.

A more basic subject-first version would be:

Hendes jakke hænger ved brusekabinen i omklædningsrummet.

Both are grammatical, but they focus slightly differently:

• I omklædningsrummet hænger hendes jakke ... puts the location first
• Hendes jakke hænger ... starts with the subject and sounds a bit more neutral

Danish often moves time or place to the front when that information is important.

Because sin/sit/sine is a reflexive possessive, used when the owner is the subject of the clause.

In this sentence, the subject is:

• hendes jakke

So there is no subject like hun that could trigger sin.

That is why hendes is correct here.

Compare:

• Hun hænger sin jakke ved brusekabinen.
  = She hangs her own jacket by the shower cubicle.

• Hun hænger hendes jakke ved brusekabinen.
  = She hangs her jacket, but standard Danish usually suggests it belongs to another female person, not to the subject herself.

So in your sentence, hendes simply means her.

Because a possessive already does the job that an article would do.

So Danish says:

• hendes jakke = her jacket

Not:

• den hendes jakke

This is the same idea as in English: we say her jacket, not the her jacket.

hænger is the present tense of at hænge.

Here it means:

• hangs
• or in natural English, is hanging

So:

• hendes jakke hænger = her jacket is hanging

Danish often prefers a specific position verb such as:

• står = stands
• ligger = lies/is lying
• hænger = hangs/is hanging

Instead of using a more general verb like is.

So hænger is more natural than er here because a jacket is in a hanging position.

Here ved means something like:

• by
• near
• next to

So:

• ved brusekabinen = by the shower cubicle / near the shower cubicle

It does not mean the jacket is inside the cubicle. It means it is located close to it.

Because Danish usually expresses the by adding it to the end of the noun.

So:

• et omklædningsrum = a changing room
• omklædningsrummet = the changing room

And:

• en brusekabine = a shower cubicle
• brusekabinen = the shower cubicle

In this sentence, the speaker is referring to specific places in the situation, so the definite forms are used.

The basic forms are:

• et omklædningsrum = a changing room
• en jakke = a jacket
• en brusekabine = a shower cubicle / shower stall

Their forms in the sentence are:

• omklædningsrummet = definite singular
• hendes jakke = singular with a possessive
• brusekabinen = definite singular

This is useful because when you look words up in a dictionary, you usually need the indefinite singular form: omklædningsrum, jakke, brusekabine.