Kan du række mig de der bøger?

Because Danish yes/no questions normally use verb + subject order.

• Statement: Du kan række mig de der bøger.
• Question: Kan du række mig de der bøger?

This works a lot like English:

• You can pass me those books.
• Can you pass me those books?

It can be both, just like English Can you ...?

In this sentence, it is most naturally understood as a request, not as a serious question about ability. So Kan du række mig de der bøger? is a normal everyday way to say Can you pass me those books?

Here, række means something like pass, hand, or reach over.

So række mig de der bøger means pass me those books or hand me those books.

It is especially natural when:

• the other person can physically reach the item
• you want them to hand it to you

A close alternative is give, but række often sounds more specifically like hand over / pass across.

Because mig is the object form of jeg.

• jeg = I
• mig = me

After the verb række, you need me, not I, so Danish uses mig:

• Kan du række mig ... ? = Can you pass me ... ?

In Danish, when you have a verb like række and a short pronoun such as mig, it is very common for the receiver to come before the thing being passed.

So:

• række mig de der bøger = pass me those books

This is very natural Danish word order.

You can also say:

• Kan du række de der bøger til mig?

That also means Can you pass those books to me? It is perfectly correct, but the version with mig before the noun phrase is especially common and natural.

de der means those or more literally those there.

• de = plural demonstrative
• der adds the idea of there / over there

So:

• de der bøger = those books
• de her bøger = these books

In everyday spoken Danish, de der is a very common way to point out books that are farther away, already visible, or already being referred to.

In standard Danish, when the demonstrative comes before a noun, you normally use de:

• de der bøger = those books

dem der is normally used when the noun is left out:

• Kan du række mig dem der? = Can you pass me those?

You may hear dem der bøger in some varieties of spoken Danish, but it is not standard.

Because after demonstratives like den, det, de, den her, den der, de her, and de der, Danish normally uses the noun without the ending -en / -et / -ne.

So you say:

• de der bøger
• not de der bøgerne

Compare:

• bøgerne = the books
• de der bøger = those books

This is a very important Danish pattern.

Yes, it is the same Danish word, and the meaning is related.

On its own, der can mean there:

• Bøgerne er der. = The books are there.

But in de der bøger, it is part of a demonstrative expression meaning those books or those books there.

So in this sentence, der is not standing alone as a location word; it is helping form the idea those.

Yes. You could say:

• Kan du give mig de der bøger?

That is understandable and natural.

The difference is mainly nuance:

• give = give
• række = hand / pass / reach over

If someone is nearby and you want them to hand something to you, række is often the most precise word.

Yes. Kan du række mig de der bøger? is a normal, natural everyday request.

It is not rude. It sounds fine in ordinary situations.

If you want to sound softer or more polite, you could say:

• Kunne du række mig de der bøger? = Could you pass me those books?
• Vil du række mig de der bøger? = Will/Would you pass me those books?
• Vil du være sød at række mig de der bøger? = Would you be so kind as to pass me those books?

You just change the demonstrative and noun form:

• Kan du række mig den der bog? = Can you pass me that book?
• Kan du række mig de her bøger? = Can you pass me these books?
• Kan du række mig denne bog? = Can you pass me this book?
  This is more formal than den her bog.

So the pattern is:

• den der bog = that book
• de der bøger = those books
• den her bog = this book
• de her bøger = these books