Jeg kan lide både teatret og parken, fordi der er ro på bænken ved dammen og liv på scenen.

In Danish, kan lide is a fixed expression meaning to like.

So:

• Jeg kan lide teatret = I like the theatre
• Jeg kan lide parken = I like the park

Even though kan on its own usually means can / be able to, in kan lide you should learn the whole phrase together. Very often Danes also say kan godt lide, which sounds especially natural in everyday speech:

• Jeg kan godt lide teatret = I like the theatre

Både ... og ... means both ... and ....

In the sentence:

• både teatret og parken = both the theatre and the park

It is used to connect two things that are both included. The structure is very straightforward:

• både X og Y = both X and Y

In Danish, the definite article is usually attached to the end of the noun.

So:

• teater = a theatre

• teatret = the theatre

• park = a park
• parken = the park

This is one of the biggest differences from English. Instead of putting the before the noun, Danish often adds a definite ending to the noun itself.

Because Danish nouns have grammatical gender, and the definite ending depends on the gender.

• et teater → teatret
  This is a neuter noun, so the definite ending is usually -et.

• en park → parken
• en bænk → bænken
• en dam → dammen
• en scene → scenen
  These are common gender nouns, so the definite ending is usually -en.

So the endings are not random; they match the noun’s gender.

Der er is the normal Danish way to say there is or there are.

So:

• der er ro = there is calm
• der er liv = there is life / activity

By contrast, det er usually means it is. So in this sentence, der er is correct because the sentence is introducing the existence of something: calm in one place and liveliness in another.

Here they are being used in a slightly descriptive, atmospheric way.

• ro means calm, peace, quiet, or stillness
• liv literally means life, but in this kind of sentence it often means activity, energy, or liveliness

So the contrast is:

• calm by the pond
• lively activity on the stage

It is a nice stylistic contrast: the park offers peace, while the theatre offers energy.

The prepositions match the physical relationship:

• på bænken = on the bench
• ved dammen = by / near the pond
• på scenen = on the stage

So:

• på is used for being on a surface or platform
• ved is used for being beside or near something

These are very natural choices in Danish, just as they are in English.

Because the sentence presents them as specific, identifiable places in the scene being described.

• på bænken = on the bench
• ved dammen = by the pond
• på scenen = on the stage

Using the definite form makes the image more concrete. It sounds like we are talking about a particular bench by a particular pond, and the stage connected with the theatre.

Because teatret and parken are the direct objects of kan lide.

The sentence means:

• I like the theatre
• I like the park

If you said i teatret, that would mean in the theatre, which would describe location instead of what is being liked.

So:

• Jeg kan lide teatret = I like the theatre
• Jeg er i teatret = I am in the theatre

That is an important difference.

In this sentence, scenen means the stage.

Although Danish scene is related to English scene, in theatre contexts it commonly means the physical stage. So:

• på scenen = on the stage

This is a good example of a word that looks familiar to an English speaker but is used a bit differently.

Fordi means because and introduces the reason.

So the sentence has this structure:

• Jeg kan lide både teatret og parken = main statement
• fordi ... = explanation/reason

In standard Danish grammar, fordi introduces a subordinate clause. In this particular sentence, that is not very noticeable because der er looks the same as it would in a main clause. But in other sentences, subordinate-clause word order becomes clearer, for example:

• Jeg kan ikke lide støj. = main clause
• ..., fordi jeg ikke kan lide støj. = subordinate clause

That difference is worth noticing as you learn.

Yes, absolutely. That would sound very natural.

Godt is often added in everyday Danish with kan lide:

• Jeg kan godt lide teatret
• Jeg kan godt lide parken

It does not usually mean well in a literal way here. It simply makes the expression more idiomatic and natural. Without godt, the sentence is still completely correct.

Yes, but in a positive way.

The sentence says the speaker likes both places for different reasons:

• the park has ro: peace and quiet
• the theatre has liv: energy and activity

So the sentence is built on a contrast between calm and liveliness, but both are presented as attractive. That is why både ... og ... fits so well here.