Jeg kan ofte trøste barnet med en bamse og en stille vuggevise.

Because Danish main clauses usually follow the V2 rule: the finite verb comes second.

In Jeg kan ofte trøste barnet ...:

• Jeg = first element
• kan = finite verb, so it comes second

This is very normal in Danish. Even if you move something else to the front, the finite verb still stays in second position:

• Ofte kan jeg trøste barnet ...

So kan is second because Danish main clauses are built that way.

After a modal verb like kan (can), Danish uses the bare infinitive—that means the infinitive without at.

So:

• kan trøste = can comfort
• not kan at trøste

This is similar to English:

• I can comfort
• not I can to comfort

Other modal verbs work the same way:

• jeg vil trøste = I want to comfort / I will comfort
• jeg må trøste = I must comfort
• jeg skal trøste = I have to / will comfort

Ofte means often. It is an adverb of frequency.

In this sentence, it comes after the finite verb kan:

• Jeg kan ofte trøste barnet ...

That placement is very typical in Danish. Sentence adverbs like ofte, ikke, altid, sjældent often appear after the finite verb in a main clause.

Compare:

• Jeg kan ofte trøste barnet. = I can often comfort the child.
• Jeg kan ikke trøste barnet. = I cannot comfort the child.

So ofte is in a very natural Danish position.

Yes, but the meaning or emphasis may change a little, and some placements sound more natural than others.

The most neutral version here is:

• Jeg kan ofte trøste barnet ...

You could also front it for emphasis:

• Ofte kan jeg trøste barnet ...

That sounds more marked, like Often, I can comfort the child ...

A version like Jeg kan trøste barnet ofte is much less natural in this meaning. Danish usually prefers ofte earlier in the clause rather than at the very end.

Because barnet is the definite singular form of barn.

• et barn = a child
• barnet = the child

Danish usually makes a noun definite by adding an ending:

• en bog = a book → bogen = the book
• et hus = a house → huset = the house
• et barn = a child → barnet = the child

So barnet tells you the speaker means a specific child, not just any child.

Because barn is a neuter noun in Danish, and the definite singular ending for many neuter nouns is -et.

• et barn = a child
• barnet = the child

Compare with common-gender nouns, which usually take -en:

• en bamse = a teddy bear
• bamsen = the teddy bear

So the ending depends on the noun’s grammatical gender.

Because Danish nouns belong to different grammatical genders.

• bamse is common gender → en bamse
• barn is neuter → et barn

This is something you usually have to learn together with each noun. A good habit is to memorize nouns with their article:

• en bamse
• et barn
• en vuggevise

That makes it easier to build correct phrases later.

Here med means with in the sense of using something as a means to comfort the child.

So the idea is:

• comforting the child with a teddy bear
• and with a quiet lullaby

It does not mainly mean that the speaker is accompanied by those things in the sense of together with. It is more like the teddy bear and lullaby are tools or means of comfort.

Yes. The whole prepositional phrase explains how or by what means the child is comforted.

The structure is basically:

• Jeg kan ofte trøste barnet
• med en bamse og en stille vuggevise

So both en bamse and en stille vuggevise are things used to comfort the child.

Because these are two separate singular countable nouns, and each one normally gets its own indefinite article.

• en bamse = a teddy bear
• en stille vuggevise = a quiet lullaby

So Danish, like English, says:

• a teddy bear and a quiet lullaby

not normally:

• a teddy bear and quiet lullaby

Stille is the adjective meaning quiet, gentle, or soft here.

In this phrase:

• en stille vuggevise

the adjective is simply in its normal form. Many Danish adjectives ending in -e look the same in several forms, and stille is one of them.

So you just learn the phrase as:

• en stille vuggevise = a quiet lullaby

There is no extra visible change needed here.

Vuggevise means lullaby.

It is a compound noun:

• vugge = cradle
• vise = song / ballad

So literally it is something like a cradle-song, which is why it means lullaby.

Danish uses compound nouns very often, so this is a useful example of how smaller words combine into one larger noun.

Trøste usually means comfort or console someone who is upset, sad, scared, or crying.

In this sentence, comfort is probably the most natural English idea, especially because the object is barnet and the comforting is done with a teddy bear and a lullaby.

So it suggests soothing or calming the child.

Here kan most naturally expresses ability or what is often possible for the speaker to do.

So the sense is something like:

• I am often able to comfort the child ...
• I can often comfort the child ...

It does not strongly suggest permission here. It is about what the speaker is capable of doing successfully.

Yes, quite similar, which is helpful for English speakers.

Word by word, it is roughly:

• Jeg = I
• kan = can
• ofte = often
• trøste = comfort
• barnet = the child
• med = with
• en bamse = a teddy bear
• og = and
• en stille vuggevise = a quiet lullaby

So the structure is fairly close to English, though Danish word order rules—especially the position of the finite verb and adverbs—are stricter in some ways.

The normal negative word is ikke, and it usually goes in the same area where ofte appears.

A natural negative version would be:

• Jeg kan ikke ofte trøste barnet med en bamse og en stille vuggevise.

But that means I cannot often comfort the child..., which is a bit unusual in English too.

More natural possibilities, depending on meaning, might be:

• Jeg kan ikke trøste barnet med en bamse og en stille vuggevise.
  = I cannot comfort the child with a teddy bear and a quiet lullaby.

• Jeg kan ofte ikke trøste barnet med en bamse og en stille vuggevise.
  = I often cannot comfort the child with a teddy bear and a quiet lullaby.

So the position of ikke matters for the meaning.