Vi vil sælge det gamle bord, men beholde den nye sofa.

Because Danish nouns have grammatical gender.

• bord is a neuter noun, so it takes det
• sofa is a common gender noun, so it takes den

So:

• det gamle bord = the old table
• den nye sofa = the new sofa

A useful pattern is:

• den
  • adjective + common-gender noun
• det
  • adjective + neuter noun

Without the adjective, you would usually say:

• bordet = the table
• sofaen = the sofa

But when an adjective comes before the noun, Danish normally uses den/det/de + adjective + noun instead.

In this sentence, the nouns are in a definite phrase: the old table, the new sofa.

When an adjective comes before a definite noun in Danish, the adjective normally takes -e:

• det gamle bord
• den nye sofa

This -e ending is very common in definite phrases.

Compare:

• et gammelt bord = an old table

• det gamle bord = the old table

• en ny sofa = a new sofa
• den nye sofa = the new sofa

So the adjective changes depending on the structure:

• indefinite singular common gender: often base form, e.g. ny
• indefinite singular neuter: often -t, e.g. gammelt
• definite: usually -e, e.g. gamle, nye

Because vil is a modal verb meaning want to / will depending on context, and after modal verbs, Danish uses the bare infinitive.

So:

• vi vil sælge = we want to sell / we will sell
• vi vil beholde = we want to keep / we will keep

There is no at after modal verbs such as:

• vil
• kan
• skal
• må
• bør

Examples:

• Jeg kan svømme. = I can swim.
• Hun skal arbejde. = She has to work.

So vil sælge is correct, not vil at sælge.

It can mean either, depending on context.

In many everyday sentences like this one, vil often sounds like want to:

• Vi vil sælge det gamle bord = We want to sell the old table

But in some contexts it can also be understood as a future meaning:

• We will sell the old table

If the sentence is presented as a plan or intention, English might translate it either way. Danish often uses vil where English would choose between want to and will based on context.

Because Danish, like English, often avoids repeating words that are understood already.

So:

• Vi vil sælge det gamle bord, men beholde den nye sofa.

means the same as:

• Vi vil sælge det gamle bord, men vi vil beholde den nye sofa.

The shorter version is natural and common. The second infinitive beholde is understood to depend on the same vil.

This is similar to English:

• We want to sell the old table but keep the new sofa.

You do not have to repeat want to.

Yes. In this sentence, men means but, and it connects two parts of the sentence.

Here the second part is shortened:

• men beholde den nye sofa

This is understood as:

• men vi vil beholde den nye sofa

Because the subject and modal verb are already clear from the first part, they are omitted.

If you do include them, normal main-clause word order applies:

• Vi vil sælge det gamle bord, men vi vil beholde den nye sofa.

So there is nothing strange here—just a coordinated structure with omitted repeated words.

Because in Danish, adjectives usually come before the noun, like in English.

So:

• det gamle bord = literally the old table
• den nye sofa = literally the new sofa

The normal order is:

• den/det/de
  • adjective + noun

You do not usually put the adjective after the noun in this kind of phrase.

Also, when there is an adjective, Danish normally uses the separate definite article den/det/de before the adjective, instead of attaching definiteness directly to the noun:

• bordet = the table
• det gamle bord = the old table

Beholde means to keep, to retain, or to hang on to something instead of getting rid of it.

In this sentence:

• beholde den nye sofa = keep the new sofa

It suggests that they are deciding not to sell the sofa.

A useful contrast is:

• sælge = to sell
• beholde = to keep

So the sentence sets up a contrast:

• sell the old table
• keep the new sofa

Yes, absolutely.

That version is fully correct and may sound a bit more explicit because it repeats vi vil.

Compare:

• Vi vil sælge det gamle bord, men beholde den nye sofa.
• Vi vil sælge det gamle bord, men vi vil beholde den nye sofa.

Both are natural. The shorter version is just more compact.

A few words may be hard for English speakers:

• vi sounds roughly like vee
• vil sounds roughly like vil with a short i
• sælge has the Danish letter æ, somewhat like the vowel in English cat, though not exactly
• gamle is roughly GAM-luh, with the second syllable weak
• nye is roughly NYE-uh or new-eh, though the real Danish pronunciation is smoother than that
• beholde is roughly beh-HOL-duh
• sofa is close to English sofa, but with Danish vowel quality

The hardest part is usually not the individual sounds alone, but the reduced endings like -e in gamle, nye, and beholde, which are often pronounced very lightly.

The structure is:

• Vi = subject
• vil = modal verb
• sælge = infinitive verb
• det gamle bord = object
• men = conjunction
• beholde = second infinitive linked to vil
• den nye sofa = object

So a simple breakdown is:

We + want to / will + sell + the old table, but + keep + the new sofa

This is a very useful Danish pattern:

• subject + modal verb + infinitive
• and then another infinitive after og or men if the modal still applies

For example:

• Jeg vil spise og drikke. = I want to eat and drink.
• Hun kan læse, men ikke skrive. = She can read, but not write.