Hun hænger sin jakke på en tøjbøjle og lægger skjorten i kommoden.

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

So in Hun hænger sin jakke ..., the subject is hun, and the jacket belongs to that same person. That is why Danish uses sin.

• Hun hænger sin jakke ... = she hangs her own jacket ...
• Hun hænger hendes jakke ... would usually mean she hangs another woman’s jacket

A very important point: sin matches the thing owned, not the owner.

• sin jakke because jakke is a common-gender singular noun
• sit tøj because tøj is neuter
• sine sko because sko is plural

This is about definiteness: whether Danish means the or a/an.

• skjorten = the shirt
• kommoden = the dresser / the chest of drawers
• en tøjbøjle = a clothes hanger

In Danish, the definite article is usually added to the end of the noun:

• skjorte = shirt

• skjorten = the shirt

• kommode = dresser / chest of drawers
• kommoden = the dresser

But for indefinite nouns, Danish uses a separate article before the noun:

• en tøjbøjle = a clothes hanger

So the sentence is mixing definite and indefinite nouns because the meaning requires it: she puts the jacket on a hanger, and puts the shirt in the dresser.

They are two different verbs because the objects are placed in different positions.

• hænge = to hang
• lægge = to lay / put down / place lying

So:

• Hun hænger sin jakke på en tøjbøjle = she hangs her jacket on a hanger
• ... og lægger skjorten i kommoden = and puts the shirt in the dresser

Danish often uses different placement verbs depending on the position of the thing:

• lægge for something placed lying down
• sætte for something placed sitting/upright
• stille for something stood up
• hænge for something hung

English often just uses put, but Danish is more specific.

Because the prepositions reflect the physical relationship.

• på = on
• i = in

A jacket goes on a hanger, so Danish says på en tøjbøjle.

A shirt goes in a dresser, so Danish says i kommoden.

This matches English quite closely here:

• on a hanger
• in the dresser

So this part is quite straightforward.

It is in the present tense.

• hænger = present tense of hænge
• lægger = present tense of lægge

In Danish, the present tense is usually formed by adding -r to the infinitive:

• at hænge → hænger
• at lægge → lægger

So the sentence means something like She hangs her jacket on a hanger and puts the shirt in the dresser, or depending on context, it can also describe a habitual action: She hangs her jacket... and puts the shirt...

Because the same subject applies to both verbs.

• Hun hænger ... og lægger ...

This means She hangs ... and puts ...

In English, you also normally say:

• She hangs her jacket and puts the shirt away not
• She hangs her jacket and she puts the shirt away

Danish works the same way here. Once the subject is clear, it does not need to be repeated before the second verb.

This is normal Danish main-clause word order. Danish is a verb-second language in main clauses, often called V2.

In a simple statement, the pattern is usually:

• subject + verb + rest

So:

• Hun hænger sin jakke ...
• Hun lægger skjorten ...

If something else comes first, the verb still usually stays in second position:

• I kommoden lægger hun skjorten.

That sounds more marked, but it shows the rule clearly: the finite verb stays in the second slot.

Tøjbøjle is a compound noun:

• tøj = clothes
• bøjle = hanger / frame / bracket, depending on context

Together, tøjbøjle means clothes hanger.

Compound nouns are very common in Danish, just like in German. English often writes these as separate words, but Danish often combines them into one word.

So:

• tøjbøjle = clothes hanger

You may also hear simply bøjle in everyday speech if the context is obvious.

Because Danish does not need it here.

English often uses particle verbs like:

• hang up
• put away
• take off

Danish often expresses the same idea with just the main verb and a prepositional phrase:

• hænge jakken på en bøjle
• lægge skjorten i kommoden

So Danish does not need a separate word for up in this sentence. The idea is already clear from hænger plus på en tøjbøjle.

Because the ending -en marks the definite form for many common-gender nouns.

• en kommode = a dresser
• kommoden = the dresser

This is one of the first big differences English speakers notice in Danish: the definite article is often attached to the noun instead of standing as a separate word.

The same pattern appears in:

• en stol → stolen
• en jakke → jakken
• en skjorte → skjorten

Yes, often you can.

Bøjle by itself can mean hanger, and in many everyday situations that is enough.

• Hun hænger sin jakke på en bøjle is natural
• Hun hænger sin jakke på en tøjbøjle is a bit more specific: on a clothes hanger

So tøjbøjle is more explicit, but bøjle is often perfectly normal if the context makes it clear.

Not always exactly. Vocabulary does not always match one-to-one across languages.

Kommode usually refers to a piece of furniture with drawers, often translated as:

• chest of drawers
• dresser

Which English word fits best depends on the variety of English and the context. But grammatically, there is nothing unusual here: i kommoden just means in the dresser / chest of drawers.

A rough guide for English speakers:

• hænger sounds roughly like HENG-er, but with a Danish æ sound, which is more open than English e
• lægger sounds roughly like LEG-er, again with Danish æ

A few useful sound notes:

• æ is somewhat like the vowel in English cat, though not exactly
• ø in tøjbøjle has no exact English equivalent; it is a rounded front vowel
• j in Danish is pronounced like English y

So tøjbøjle is roughly something like TOY-boi-leh, but that is only a rough approximation. Danish pronunciation can differ a lot from spelling, so listening to native audio is especially helpful here.