Min søster prøver at trøste hende, når sutten falder på gulvet.

In Danish, a possessive like min, din, hans, hendes, etc. usually replaces the article. So:

• min søster = my sister
• not min søsteren

You normally do not use both a possessive and the suffixed definite ending together in this kind of phrase.

After many verbs in Danish, the next verb appears in the infinitive, often with at.

Here:

• prøver = tries / is trying
• at trøste = to comfort

So prøver at trøste means tries to comfort.

This is very similar to English try to do something.

Because hende is the object form of the pronoun, while hun is the subject form.

• hun = she
• hende = her

In this sentence, the sister is doing the comforting, and her is receiving the action, so Danish uses hende.

Compare:

• Hun trøster barnet. = She comforts the child.
• Barnet ser hende. = The child sees her.

Når is used for when in the sense of something that happens regularly, repeatedly, or whenever a situation occurs.

So here it means something like:

• when / whenever the pacifier falls on the floor

That fits because this is probably a repeated situation, not one single past event.

A useful contrast:

• når = when something generally happens or will happen
• da = when something happened once in the past

Because sutten is the definite form: the pacifier / the dummy.

In Danish, definiteness is often shown by adding an ending to the noun:

• en sut = a pacifier
• sutten = the pacifier

So instead of a separate word like English the, Danish often adds -en or -et to the noun.

Falder is the present tense of falde (to fall).

• falde = infinitive, to fall
• falder = present tense, falls / is falling

In Danish, the present tense often ends in -r.

Here the present tense can describe a general repeated situation, not only something happening right this second.

Because Danish, like English, often uses the present tense for habitual or repeated events.

So når sutten falder på gulvet does not have to mean one specific fall happening right now. It can mean:

• whenever the pacifier falls on the floor
• when that kind of thing happens

This is a normal way to describe routines or recurring situations.

Gulvet is the definite form of gulv:

• et gulv = a floor
• gulvet = the floor

Danish often uses the definite form where English also says the floor. In this sentence, it refers to the floor in the situation, so på gulvet is the natural phrasing.

Because når sutten falder på gulvet is a subordinate clause.

Danish comma usage often marks the boundary before a subordinate clause. You will frequently see a comma before words like:

• at
• fordi
• hvis
• når
• som

So the comma here helps separate:

• main clause: Min søster prøver at trøste hende
• subordinate clause: når sutten falder på gulvet

Then the main clause would follow normal Danish inversion rules.

You could say:

• Når sutten falder på gulvet, prøver min søster at trøste hende.

Notice what happens in the main clause after the initial subordinate clause:

• prøver min søster
• not min søster prøver

This is because Danish is a V2 language: when something other than the subject comes first, the finite verb usually comes before the subject in the main clause.

It is followed directly by the object. So:

• trøste hende = comfort her

No extra preposition is needed.

That is similar to English comfort someone, not comfort to someone.

Yes. In this kind of sentence, English might naturally say either:

• when the pacifier falls on the floor
• whenever the pacifier falls on the floor

Danish når covers that general repeated meaning very well here.