Jeg kan godt lide måden, hun forklarer teksten på.

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

So:

• Jeg kan godt lide kaffe = I like coffee
• Jeg kan godt lide måden ... = I like the way ...

It is not usually understood literally as I am able to like. Native speakers hear it as a normal way to express liking.

You can also say jeg elsker for I love, but jeg kan godt lide is the everyday neutral way to say I like.

Here godt is part of the idiomatic expression kan godt lide. It does not simply mean well in the usual English sense.

Compare:

• Jeg kan lide det = I like it
• Jeg kan godt lide det = I like it

Both are possible, but kan godt lide is extremely common and often sounds more natural in everyday Danish.

So in this sentence, it is best to learn kan godt lide as one chunk.

Because the sentence refers to a specific way: the way she explains the text.

• en måde = a way
• måden = the way

The clause after it identifies which way is meant:

• måden, hun forklarer teksten på = the way she explains the text

So the definite form måden is required here.

The noun is:

• en måde = a way

It is a common-gender noun, and its definite singular form is:

• måden = the way

So:

• indefinite: en måde
• definite: måden

In this sentence, Danish uses the definite form because the following clause specifies it.

The comma separates the main noun phrase from the clause that explains it:

• måden, hun forklarer teksten på

This clause tells us which way we mean.

Danish comma rules can vary depending on whether someone uses traditional comma or new comma, but in teaching materials you will often see a comma before this kind of subordinate or relative-like clause. So this punctuation is normal and expected.

Danish often leaves out a relative word in this kind of structure.

English says:

• the way she explains the text

and Danish can do something very similar:

• måden, hun forklarer teksten på

You may also see fuller versions such as:

• den måde, som hun forklarer teksten på
• måden, hvorpå hun forklarer teksten

But the version in your sentence is very natural and common.

Because it belongs with måden and with the idea of the way in which something is done.

Literally, the structure is something like:

• the way she explains the text in/on/by

That sounds odd in English, but it is normal in Danish to leave the preposition at the end in this kind of clause.

So:

• måden, hun forklarer teksten på

is a very natural Danish pattern.

You can think of på here as part of the expression meaning the way ...

Yes. That is also correct and natural.

Compare:

• Jeg kan godt lide måden, hun forklarer teksten på.
• Jeg kan godt lide den måde, hun forklarer teksten på.

Both mean essentially the same thing: I like the way she explains the text.

The version with den måde can feel a little more explicit, while måden alone is also very idiomatic and common.

Because this is a subordinate clause after måden, and the subject comes before the verb:

• hun = subject
• forklarer = verb
• teksten = object
• på = preposition left at the end

So the order is:

hun + forklarer + teksten + på

This is normal Danish clause structure here.

Notice that unlike in a main clause, there is no inversion. Compare:

• main clause: Hun forklarer teksten på en god måde.
• inside this phrase: måden, hun forklarer teksten på

Because it refers to a specific text, not just any text.

• en tekst = a text
• teksten = the text

So the sentence means she is explaining a particular text that speaker and listener already know about, or that has already been mentioned.

If it were not specific, you might say:

• hun forklarer en tekst = she explains a text

But that would change the meaning.

Yes, you can. It is grammatically correct.

• Jeg kan lide ...
• Jeg kan godt lide ...

Both can mean I like ...

But kan godt lide is more idiomatic and very common in everyday Danish. Many learners are taught it as the standard way to say like.

So dropping godt is possible, but the full expression often sounds more natural.

Yes, this is natural Danish.

A few natural alternatives are:

• Jeg kan godt lide måden, hun forklarer teksten på.
• Jeg kan godt lide den måde, hun forklarer teksten på.
• Jeg synes, hun forklarer teksten godt.

The last one shifts the wording a bit and means more directly:

• I think she explains the text well

So your original sentence is perfectly natural, especially if you want to focus specifically on the way she does it.

Not exactly. The main verb is forklarer = explains.

The på does not primarily belong to forklarer itself. Instead, it belongs to the larger pattern with måde/måden:

• måden ... på = the way ...

So it is better to understand this as a construction:

• måden, hun forklarer teksten på

rather than as a special verb forklare på in this sentence.