Min niece kan ikke nå den øverste hylde endnu, så jeg rækker hende kassen, når hun beder om den.

Because niece is a common-gender noun in Danish. Singular possessives agree with the gender of the noun:

• min = for common gender
• mit = for neuter

So:

• min niece = my niece
• mit barn = my child

Here, nå means to reach in the physical sense.

So kan ikke nå den øverste hylde endnu means cannot reach the top shelf yet.

Be careful: nå can also mean other things in other contexts, such as to arrive, to manage to, or even an interjection like oh/well in conversation. But in this sentence it clearly means reach.

In Danish main clauses, the negation ikke usually comes after the finite verb.

Here the finite verb is kan, so you get:

• kan ikke nå

This is very normal Danish word order. English often says cannot reach, but Danish separates the modal verb and the negation:

• hun kan ikke nå = she cannot reach

In this sentence, endnu means yet.

• kan ikke nå ... endnu = cannot reach ... yet

This is a very common pattern in Danish:

• ikke ... endnu = not ... yet

In other contexts, endnu can sometimes feel closer to still or even, but here yet is the natural meaning.

There are two important things happening here:

1. hylde is a common-gender noun, so the definite article used before it is den
2. øverste is the adjective form used in a definite noun phrase

So:

• en hylde = a shelf
• den øverste hylde = the top shelf / the uppermost shelf

The adjective gets the -e ending because it comes after a definite determiner like den.

Because øverste is the adjective form used before a noun in a definite phrase:

• den øverste hylde = the top shelf

But øverst is often used as an adverb or as a predicate:

• Hylden er øverst. = The shelf is at the top.

So:

• before the noun: øverste
• standing on its own in many cases: øverst

Here, så means so in the sense of therefore / as a result.

The sentence structure is:

• She can't reach the top shelf yet, so I hand her the box ...

Danish så is very commonly used this way to connect cause and result.

Here, rækker comes from at række, which means to hand, to pass, or to reach/give something to someone by stretching it toward them.

So:

• jeg rækker hende kassen = I hand her the box

It is not the same as give in all situations, though it can overlap in meaning. Række often suggests physically passing something over.

Both are possible.

• jeg rækker hende kassen
• jeg rækker kassen til hende

The first version uses the pattern verb + person + thing, which is very common in Danish with verbs like give, show, send, and række.

The second version uses til hende and can sound a little more explicit.

So the sentence’s version is natural and idiomatic. It works like English I hand her the box.

Because Danish distinguishes between subject and object pronouns.

• hun = she used as a subject
• hende = her used as an object

So:

• når hun beder om den = when she asks for it
  Here hun is the subject of beder

• jeg rækker hende kassen = I hand her the box
  Here hende is the indirect object

This is just like English she/her.

Because når is used for something that is expected, repeated, or seen as a regular occurrence: when.

In this sentence, the meaning is something like:

• whenever she asks for it
• when she asks for it

So når fits well.

Hvis means if and is used for a more uncertain condition:

• Hvis hun beder om den, rækker jeg hende kassen.
  = If she asks for it, I hand her the box.

That version is possible, but it gives a slightly different feel. The original sentence sounds more like a normal repeated situation.

Because the verb is at bede om, which means to ask for.

So:

• bede om noget = ask for something

Examples:

• Hun beder om vand. = She asks for water.
• Han bad om hjælp. = He asked for help.

You cannot normally drop om here, because it is part of the standard expression.

Den refers back to kassen.

• kasse is a common-gender noun
• so the pronoun used for it is den

That is why the sentence says:

• hun beder om den = she asks for it

If the noun were neuter, Danish would use det instead.

Because Danish often uses the present tense for habitual or general repeated actions, just like English.

So the sentence does not necessarily mean this is happening only right now. It means something more like a regular pattern:

• She still cannot reach the top shelf, so I hand her the box when she asks for it.

This is very natural in both Danish and English.

No. After a possessive like min, Danish normally uses the noun without the definite ending.

So:

• min niece = my niece

Not:

• min niesen

This is similar to English, where we say my niece, not my the niece.

The same pattern applies broadly:

• min bog = my book
• hendes bil = her car
• vores hus = our house

Yes. kassen is the definite singular form of kasse.

• en kasse = a box
• kassen = the box

So in the sentence:

• jeg rækker hende kassen = I hand her the box

Danish usually adds the definite ending directly to the noun, instead of using a separate word like English the.