Jeg kan godt lide at høre rolig musik og læse samtidig.

This is one of the most common things learners ask.

In Danish, at kunne lide / at kan lide in everyday use is an idiomatic way to say to like. So in this sentence, jeg kan godt lide ... simply means I like ...

About godt:

• Jeg kan lide ... = I like ...
• Jeg kan godt lide ... = also I like ..., but this is often the more natural everyday phrasing

The godt does not always need a separate English translation. It often adds a natural, slightly warmer or softer tone, something like quite / really / rather, depending on context.

So you should learn kan godt lide as a very common chunk.

Because Danish, like English, often uses one infinitive marker for two coordinated verbs.

Here the structure is:

• at høre rolig musik og læse samtidig

That works like English:

• to listen to calm music and read at the same time

You do not need to repeat at before the second verb when the two verbs are linked by og and belong together.

So:

• at høre ... og læse ... = normal and natural

You could repeat it for emphasis in some contexts, but normally you would not.

Both can be used, but they are not exactly the same in feel.

• høre musik is a very common everyday way to say listen to music
• lytte til musik puts a bit more focus on active listening

So:

• Jeg kan godt lide at høre rolig musik = very natural
• Jeg kan godt lide at lytte til rolig musik = also correct, but a little more explicitly to listen

English usually distinguishes hear and listen more strongly than Danish does in this kind of sentence.

Because the adjective has to agree with the noun, and musik is a common-gender noun.

In Danish adjective agreement:

• common gender singular indefinite: rolig
• neuter singular indefinite: roligt

So:

• en rolig sang = a calm song
• rolig musik = calm music
• et roligt sted = a calm place

Since musik is not a neuter et-word, you do not add -t here.

Because musik is being used as an uncountable noun in a general sense, just like music in English.

Compare:

• I like calm music
• Jeg kan godt lide rolig musik

You are talking about music in general, not a music or the music.

In Danish, musik is normally not used with en in this meaning. If you wanted something more specific, you might say:

• den rolige musik = the calm music
• noget rolig musik = some calm music

But in this sentence, no article is needed.

Samtidig means simultaneously or at the same time.

In this sentence, it tells you that the speaker likes doing the two actions together:

• hearing/listening to calm music
• reading

So the idea is:

• I like listening to calm music and reading at the same time

Without samtidig, the sentence could more easily be understood as simply listing two things the speaker likes:

• I like listening to calm music and reading

With samtidig, it becomes clear that the two actions happen together.

That is a very natural place for it in Danish.

The sentence builds up like this:

• Jeg kan godt lide ...
• at høre rolig musik og læse
• samtidig

Placing samtidig at the end makes it clearly apply to the whole combination of actions. Danish often puts this kind of adverb late in the sentence.

Other placements are possible in some contexts, but this version sounds smooth and natural.

The basic Danish main-clause pattern is that the finite verb comes early, typically in second position.

Here you have:

• Jeg = subject
• kan = finite verb
• godt = adverb
• lide = infinitive/main verb part of the expression

So:

• Jeg kan godt lide ...

This is standard Danish word order for a main clause.

A useful thing to notice is that godt comes between kan and lide. That is the normal position in this expression.

If another element came first, the finite verb would still stay in second position:

• Om aftenen kan jeg godt lide at høre rolig musik og læse samtidig.

Usually rolig musik means music that feels calm, peaceful, gentle, relaxing.

It is more about the character or mood of the music than the volume.

If you want to talk about volume, Danish more often uses words like:

• stille musik = quiet music
• lav musik = low-volume music

So in this sentence, rolig musik is best understood as calm / relaxing music, not just music played quietly.

The simplest change is to remove samtidig.

Then you get:

• Jeg kan godt lide at høre rolig musik og læse.

That can mean I like listening to calm music and reading, without clearly saying that both happen simultaneously.

If you specifically want to emphasize doing them together, keep samtidig.