Fra altanen kan hun se ned i baggården.

Because Danish often puts the element you want to emphasize first. Here, Fra altanen means from the balcony, and placing it first highlights the viewpoint.

It also triggers normal Danish V2 word order: in a main clause, the finite verb comes in the second position. So after Fra altanen, the verb kan must come next:

• Fra altanen kan hun se ned i baggården.

If you start with the subject instead, you get:

• Hun kan se ned i baggården fra altanen.

Both are correct, but the first one gives a little more focus to from the balcony.

This is because of the Danish V2 rule.

In a normal main clause, the finite verb must be the second element. Since Fra altanen comes first, kan has to come second, and the subject hun comes after it:

• Fra altanen
  • kan
    • hun
      • ...

If the sentence began with hun, then you would get:

• Hun kan se ned i baggården.

So kan hun here is not a special question structure; it is just standard Danish word order after a fronted phrase.

Fra usually means from.

In this sentence, Fra altanen tells you the place from which she is looking. It gives the vantage point:

• Fra altanen = from the balcony

It does not mean movement away from the balcony here. It simply describes where she is positioned while seeing the courtyard.

Altanen is the definite form, meaning the balcony.

Danish often adds the definite article as an ending:

• en altan = a balcony
• altanen = the balcony

So Fra altanen means from the balcony, not from a balcony.

For the same reason as altanen: baggården is the definite form, meaning the courtyard or more specifically the back courtyard / inner courtyard.

Forms:

• en baggård = a courtyard / a back courtyard
• baggården = the courtyard

The ending -en marks definiteness.

A baggård is typically a courtyard behind or inside a building block, especially in older urban housing. In English, courtyard is usually the best translation.

Literally, it is made from:

• bag- = back
• gård = yard / courtyard

So it is something like back courtyard or rear courtyard, but in natural English courtyard is often enough.

Ned i means something like down into.

The word ned adds the idea of looking downward from a higher place. Since she is on a balcony, she is looking down. The preposition i means in / into, so together ned i baggården gives the image of looking down into the courtyard space.

So:

• se i baggården = see in the courtyard
• se ned i baggården = see down into the courtyard

The version with ned is more natural when the courtyard is below the speaker.

Yes, absolutely.

That version is also correct:

• Hun kan se ned i baggården fra altanen.

The difference is mostly one of emphasis and information structure:

• Fra altanen kan hun se ned i baggården.
  Focuses first on from the balcony.
• Hun kan se ned i baggården fra altanen.
  Starts more neutrally with she.

Both are natural Danish.

Kan means can.

Here it expresses ability or possibility:

• kan se = can see

So the sentence means that from the balcony, she is able to see down into the courtyard.

In some contexts, Danish uses kan in places where English might simply use the present tense, but here can see is a very natural match.

Yes, it could, but the meaning changes slightly.

• Fra altanen ser hun ned i baggården.
  This sounds more like From the balcony, she looks down into the courtyard or she sees down into the courtyard, depending on context.
• Fra altanen kan hun se ned i baggården.
  This emphasizes that the courtyard is visible from there.

So kan se often focuses on visibility or the possibility of seeing something, while ser can sound more like an actual act of looking or seeing.

It is a very common combination, but not a completely fixed idiom in the sense of having a special hidden meaning.

It is built from ordinary parts:

• se = see
• ned = down
• i = in / into

Together they describe the direction of sight: to see/look down into something.

You will find similar patterns elsewhere in Danish, for example:

• se op på himlen = look up at the sky
• se ind i rummet = look into the room
• se ud over havet = look out over the sea

In this sentence, ned is best understood as a directional adverb that goes with se to describe the direction of looking.

It is not changing the core meaning of se completely; it just adds spatial information:

• se = see
• se ned = see/look downward

Danish often uses these small directional words very naturally, and English does something similar with down, in, out, up, and so on.

A broad, learner-friendly approximation would be:

• Fra altanen → fra al-TA-nen
• kan hun → often something like kan hun with a light, reduced hun
• se ned i → se neð i
• baggården → roughly BAG-gor-den, though the real Danish vowels are harder than that spelling suggests

A few useful notes:

• g in gård is not pronounced like a hard English g.
• å sounds somewhat like the vowel in English thought for many learners, though not exactly.
• In normal speech, unstressed words like hun and i are often reduced.

If you want, the hardest word here for many English speakers is probably baggården.