Hendes lille radio står ved håndvasken, så hun kan høre musik under bruseren.

Because sin/sit/sine is a reflexive possessive that refers back to the subject of the clause.

In this sentence, the first clause’s subject is hendes lille radio, not hun. So Danish uses hendes.

Compare:

• Hun tager sin radio med. = She takes her own radio with her.
• Hendes radio står ved håndvasken. = Her radio is by the sink.

A possessive like hendes already makes the noun phrase definite, so Danish does not add en or den here.

So:

• en radio = a radio
• radioen = the radio
• hendes radio = her radio

Not en hendes radio.

Lille is the normal form of small before a singular noun in this kind of position.

It is a bit irregular, because many Danish adjectives change more predictably, but lille is very common:

• en lille radio
• et lille hus

In the plural, you would usually use små:

• små radioer

That -en is the definite article attached to the noun.

So:

• en håndvask = a sink
• håndvasken = the sink

and

• en bruser = a shower / shower head
• bruseren = the shower

Danish often puts the at the end of the noun instead of using a separate word.

Because Danish usually writes compound nouns as one word.

håndvask is made from:

• hånd = hand
• vask = wash

Together, håndvask means sink / washbasin. Then the definite ending is added: håndvasken.

Danish very often uses position verbs where English would just use is.

So står can be used for things that are standing upright or simply placed somewhere in a natural upright position.

Here, radioen står ved håndvasken means something like:

• the radio is standing by the sink
• more naturally in English: the radio is by the sink

Here ved means by, near, or next to.

So ved håndvasken means by the sink or next to the sink.

It is a very common preposition for location.

Here så means so or so that.

It links the two ideas:

• the radio is by the sink
• as a result / for the purpose that she can hear music

So the sense is: Her small radio is by the sink, so / so that she can hear music...

Because hun is the subject of the second clause, and kan is the finite verb.

So the basic structure is:

• hun = she
• kan = can
• høre = hear / listen to

This is a very normal Danish pattern with a modal verb:

• hun kan høre musik = she can hear / listen to music

Because kan adds the idea of ability or possibility: can.

• hun hører musik = she is hearing / listening to music
• hun kan høre musik = she can hear / listen to music

In this sentence, the point is that placing the radio there makes it possible for her to hear the music while showering.

Both are possible, but høre musik is very common in everyday Danish.

In many contexts, høre musik simply means listen to music.
Lytte til musik sounds a bit more like listen attentively or actively listen.

So here høre musik is completely natural.

Because musik is being used as an uncountable noun in a general sense, just like music in English.

So Danish says:

• høre musik = hear / listen to music

not høre en musik.

Literally, it means under the shower or under the shower head.

In natural English, the meaning is usually just while she is in the shower or while showering.

So it is both literal and idiomatic: the radio is placed so she can hear music while she showers.

Because Danish normally uses commas to separate clauses.

Here you have two clauses:

• Hendes lille radio står ved håndvasken
• så hun kan høre musik under bruseren

So the comma marks the boundary between them.