Det lyder, som om kopimaskinen er gået i stykker igen.

Det lyder means It sounds.

Here, det is a dummy subject, just like it in English It sounds like... It does not refer to a specific thing. Danish often uses det this way in weather expressions, general statements, and reactions.

So:

• Det lyder = It sounds
• Det lyder, som om ... = It sounds as if ...

Som om means as if.

So:

• Det lyder, som om kopimaskinen er gået i stykker igen. = It sounds as if the photocopier has broken down again.

In everyday Danish, som om is a very common way to introduce something that seems to be the case based on what you hear, see, or suspect.

Examples:

• Det ser ud, som om det regner. = It looks as if it is raining.
• Det virker, som om hun er træt. = It seems as if she is tired.

In Danish, a comma is often written before a subordinate clause, and som om kopimaskinen er gået i stykker igen is a subordinate clause.

So the comma helps mark the structure:

• main clause: Det lyder
• subordinate clause: som om kopimaskinen er gået i stykker igen

English punctuation is often lighter here, but in Danish this comma is very normal.

Kopimaskinen means the photocopier / the copy machine, while en kopimaskine means a photocopier.

The ending -en makes the noun definite:

• en kopimaskine = a photocopier
• kopimaskinen = the photocopier

This is a basic feature of Danish: the definite article is usually attached to the end of the noun instead of standing as a separate word.

Yes. Danish very often forms compound nouns as a single word.

Here:

• kopi = copy
• maskine = machine
• kopimaskine = copy machine / photocopier

Then the definite ending is added:

• kopimaskinen = the photocopier

This is very common in Danish, just as in German and the other Scandinavian languages.

Er gået i stykker means has broken down or is broken.

Literally, it looks something like has gone into pieces, but you should learn it as a fixed expression:

• gå i stykker = break, stop working, come apart
• er gået i stykker = has broken / has broken down

It can be used for machines and physical objects:

• Min telefon er gået i stykker. = My phone has broken.
• Vaskemaskinen gik i stykker. = The washing machine broke down.

Because gå is one of the verbs that forms the perfect tense with være in Danish in certain meanings, especially movement or change of state.

So:

• gå can take er in the perfect
• er gået i stykker is the normal form

This is similar to older English patterns like he is gone, and also similar to German.

So you say:

• Kopimaskinen er gået i stykker.

not

• Kopimaskinen har gået i stykker.

In this expression, er is the correct auxiliary.

Not exactly, though they are often close in meaning.

• gå i stykker means to break or to stop functioning
• ødelagt means damaged, ruined, or broken

Compare:

• Kopimaskinen er gået i stykker. = The photocopier has broken down.
• Kopimaskinen er ødelagt. = The photocopier is broken/damaged.

The first often focuses on the event or result of malfunctioning. The second describes the condition more directly.

In the subordinate clause after som om, Danish does not use main-clause V2 word order.

Main clauses in Danish usually have the finite verb in second position:

• Kopimaskinen er gået i stykker.

But after som om, the clause is subordinate, so the normal order is subject + finite verb:

• som om kopimaskinen er gået i stykker igen

This is one of the key differences between Danish main clauses and subordinate clauses.

Igen means again.

In this sentence it modifies the whole situation:

• er gået i stykker igen = has broken down again

Putting igen near the end is very natural in Danish. It often comes after the main verbal expression.

Examples:

• Han kom igen. = He came again / He came back
• Computeren virker igen. = The computer works again
• Den er gået i stykker igen. = It has broken down again

In informal writing, you may sometimes see that, but standard Danish normally writes the comma:

• Det lyder, som om ...

So if you are learning to write correctly, it is best to include it.

Yes. Even though lyder literally relates to sound, the whole expression can be used more broadly, much like English It sounds like...

It can mean:

• based on what I hear
• based on what you just said
• based on the situation

So it does not always mean you literally heard a noise from the photocopier. It can also mean that the evidence suggests that it has broken down.

Then you would use the indefinite form:

• Det lyder, som om en kopimaskine er gået i stykker igen.

That means It sounds as if a photocopier has broken down again.

Compare:

• kopimaskinen = the photocopier
• en kopimaskine = a photocopier

The original sentence with kopimaskinen suggests that both speaker and listener know which machine is being talked about.