Den lille højttaler virker igen, så min datter kan øve sin fløjte derhjemme.

Because Danish often uses double definiteness with adjectives.

When a noun is definite and has an adjective before it, Danish usually uses:

• den/det/de + adjective + noun in its basic form

So:

• højttaler = speaker
• højttaleren = the speaker

But with an adjective:

• den lille højttaler = the small speaker

You do not normally say den lille højttaleren in standard Danish.

Because højttaler is a common gender noun, it takes den, not det.

Lille is a special adjective form in Danish.

For many adjectives, you would see different endings depending on gender and definiteness, for example:

• en stor højttaler = a big speaker
• et stort hus = a big house
• den store højttaler = the big speaker

But lille is irregular and is very commonly used as the form in phrases like this:

• den lille højttaler = the small speaker

So lille is simply the correct form here.

Here, virker means works or is functioning.

So Den lille højttaler virker igen means the speaker is working again.

The verb virke can have several meanings depending on context, such as:

• to work / function
• to seem / appear
• to have an effect

In this sentence, it clearly means to function.

Because Danish main clauses usually follow V2 word order, where the finite verb comes early in the sentence, typically in second position.

So:

• Den lille højttaler = subject/topic
• virker = finite verb
• igen = adverb

This gives:

• Den lille højttaler virker igen

That placement is very natural in Danish. English also often does something similar: The small speaker works again / is working again.

Because så here means so, and it is acting as a coordinating conjunction.

After a coordinating conjunction like this, the next clause keeps normal main-clause word order:

• min datter = subject
• kan = finite verb

So:

• så min datter kan øve sin fløjte derhjemme

This is different from cases where some other element is moved to the front of the clause, which would trigger inversion.

So the sentence structure is:

• Den lille højttaler virker igen
• så min datter kan øve sin fløjte derhjemme

Both are main-clause-type word orders.

Because after a modal verb in Danish, the next verb is normally in the infinitive without at.

Common modal verbs include:

• kan = can
• skal = shall / must / is going to
• vil = will / wants to
• må = may / must
• bør = should

So you get:

• kan øve = can practice
• vil spise = wants to eat
• skal gå = must go / will go

Not:

• kan at øve

That would be ungrammatical in standard Danish.

Øve means to practice.

It is used for practicing a skill, especially music, language, performance, or something repeated to improve ability.

Examples:

• øve dansk = practice Danish
• øve sig = practice
• øve sin fløjte = practice her flute / practice playing her flute

In this sentence, the idea is that the daughter can now practice because the speaker works again.

This is a very important Danish grammar point.

Sin/sit/sine is a reflexive possessive, used when the possessor is the subject of the clause.

Here, the subject of the second clause is:

• min datter

And the flute belongs to min datter, so Danish uses the reflexive possessive:

• sin fløjte = her own flute

If you said hendes fløjte, it would usually suggest someone else’s flute, not the daughter’s own.

So:

• Min datter øver sin fløjte = My daughter practices her own flute
• Min datter øver hendes fløjte = My daughter practices her flute, but her refers to another female person

Because the form of the reflexive possessive depends on the gender and number of the noun being possessed, not on the owner.

Here the possessed noun is:

• fløjte = flute

Fløjte is a common gender singular noun, so the correct form is:

• sin fløjte

The other forms are:

• sit for neuter singular nouns
• sine for plural nouns

Examples:

• sin bog = his/her own book
• sit hus = his/her own house
• sine bøger = his/her own books

Derhjemme means at home or at her/home depending on context.

In this sentence:

• derhjemme = at home

It is commonly written as one word in Danish. It is a fixed adverb.

You may also see hjemme, which often means nearly the same thing:

• Jeg er hjemme = I am at home
• Jeg er derhjemme = I am at home

Derhjemme can sometimes feel a little more explicitly like at home there / at one’s home, but in many everyday cases the difference is small.

Because Danish usually does not combine a possessive determiner with the noun’s definite ending.

So you say:

• min datter = my daughter

not:

• min datteren

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

In Danish, possessives like min, din, hans, hendes, vores already make the noun definite enough in meaning.

Yes, højttaler is a common gender noun, which is why it takes:

• en højttaler = a speaker
• den lille højttaler = the small speaker

You often learn a Danish noun together with its article:

• en højttaler
• et hus
• en fløjte

That is the best way to remember gender, because gender affects articles, adjective agreement, and pronouns.

Not exactly in a strict grammar sense, although the meaning is close.

Here så means so, as in and as a result:

• The small speaker works again, so my daughter can practice...

If you wanted a stronger so that / in order that kind of idea, Danish might use another structure depending on context.

But in everyday English, translating this så as so is the most natural choice.

Yes.

• virker = works / is working
• kan = can / is able to
• øve = practice

So the whole sentence is in the present-time frame: the speaker is working again now, and as a result the daughter can practice at home now.

The sentence has two coordinated parts:

1. Den lille højttaler virker igen

   • subject: Den lille højttaler
   • verb: virker
   • adverb: igen

2. så min datter kan øve sin fløjte derhjemme

   • conjunction: så
   • subject: min datter
   • modal verb: kan
   • infinitive: øve
   • object: sin fløjte
   • adverb: derhjemme

So a simple breakdown is:

• [Subject] [Verb] [Adverb], så [Subject] [Modal] [Infinitive] [Object] [Adverb]

That is very natural Danish sentence structure.