Børnene har hver sit bord i det lille rum, så de kan lave lektier i ro.

Børnene means the children. The ending -ene makes it definite plural.

• et barn = a child
• børn = children
• børnene = the children

So the sentence is talking about a specific group of children, not children in general.

This is a very common Danish pattern: hver sin/sit/sine.

It means something like each their own.

So:

• hver sit bord = each has their own table/desk

Danish often expresses this idea with hver plus a possessive form that agrees with the thing owned. English usually just says each has their own desk, but Danish packages it more tightly.

Because sit agrees with the noun bord.

In Danish:

• sin is used with common-gender singular nouns
• sit is used with neuter singular nouns
• sine is used with plural nouns

Since bord is a neuter noun (et bord), the correct form is sit.

Examples:

• hver sin stol = each their own chair
• hver sit bord = each their own table/desk
• hver sine bøger = each their own books

Yes, absolutely.

Børnene har et bord hver also means The children each have a table/desk.

The difference is mostly one of phrasing:

• hver sit bord emphasizes that each child has their own separate desk
• et bord hver is a very natural alternative meaning one desk each

Both are correct and common.

Because Danish uses a different structure when a definite noun has an adjective before it.

Compare:

• rummet = the room
• det lille rum = the small room

When there is an adjective, Danish usually uses:

• definite article + adjective + noun

So:

• det = the
• lille = small
• rum = room

You do not normally say det lille rummet.

Lille is the adjective small/little, and here it is in the form used in a definite noun phrase.

In det lille rum, the whole phrase is definite, so the adjective takes the definite form. With many adjectives, that form ends in -e.

Compare:

• et lille rum = a small room
• det lille rum = the small room

So lille is the correct form here.

Here så means so or so that.

It connects the two parts:

• Børnene har hver sit bord i det lille rum
• så de kan lave lektier i ro

So the second part gives the result or purpose:

• they each have a desk in the small room, so that they can do homework in peace

Because de is the subject and kan is the verb, and this is the normal order here.

In this part:

• de = they
• kan = can

So de kan = they can

That is the standard order after så in this kind of sentence.

Yes, lave often means make, but in Danish it is also used very naturally in expressions where English would use do.

So:

• lave lektier = do homework

This is the normal Danish expression. You should learn it as a set phrase.

Other common examples:

• lave mad = cook / make food
• lave fejl = make mistakes
• lave lektier = do homework

Because Danish usually talks about homework in the plural.

• en lektie = one assignment / one piece of homework
• lektier = homework / assignments

So lave lektier is the usual way to say do homework.

This is different from English, where homework is normally uncountable.

I ro means in peace, quietly, or without being disturbed.

So:

• lave lektier i ro = do homework in peace / quietly

It is a very natural Danish expression. It often suggests calm, silence, or lack of interruption.

In this sentence, bord can very naturally be understood as desk in English.

Danish bord literally means table, but depending on context, English may translate it as desk if that sounds more natural. Since the children are doing homework, desk is often the best translation here.