Jeg forstår holdningen bedre, efter at vi har talt roligt om problemet.

In Danish, the definite article is usually added to the end of the noun as a suffix.

• holdning = attitude, opinion, stance
• holdningen = the attitude / the opinion / the stance

So jeg forstår holdningen bedre means I understand the attitude/opinion better.

You can also use den holdning, but that is more emphatic or usually needs extra information, for example:

• den holdning = that attitude / that particular opinion
• den holdning, du har = the attitude/opinion that you have

In this sentence, the simple definite form holdningen is the natural choice.

Holdning can mean several related things, depending on context:

• attitude
• opinion
• view
• stance

In this sentence, holdningen probably means something like the attitude or the position/viewpoint someone has about the problem.

So the exact English word depends on context, but the Danish word is broad enough to cover several of these ideas.

Because forstår is the present tense form of the verb at forstå (to understand).

The verb changes like this:

• at forstå = to understand
• jeg forstår = I understand
• vi forstår = we understand

So:

• Jeg forstår holdningen bedre = I understand the attitude better

If you used forstå by itself here, it would be ungrammatical, because Danish needs the finite verb form in a normal main clause.

Bedre means better. It is the comparative form of godt / god.

In this sentence, bedre functions like an adverb with the verb forstår:

• jeg forstår det = I understand it
• jeg forstår det bedre = I understand it better

So bedre does not describe the noun holdningen. It describes how well the speaker understands it.

Efter at means after when it introduces a whole clause.

Compare:

• efter mødet = after the meeting
• efter at vi har talt = after we have talked

The at is needed because what follows is a clause with its own subject and verb:

• vi = subject
• har talt = verb phrase

So:

• efter at vi har talt roligt om problemet = after we have talked calmly about the problem

Har talt is the present perfect:

• har = have
• talt = talked/spoken

Danish often uses the present perfect for something that happened before now and is relevant to the present situation.

Here, the idea is:

• first, we have talked calmly about the problem
• as a result, I understand the attitude better now

So the perfect tense fits well because the earlier conversation has a present result.

You could sometimes see a past tense like talte, but har talt sounds very natural when the speaker is focused on the present effect.

Not by itself. Talt is the past participle, not the simple past.

Forms of at tale (to speak / to talk) are:

• taler = speak / am speaking
• talte = spoke / talked
• talt = spoken / talked

So:

• vi talte = we talked
• vi har talt = we have talked

In the sentence, talt is used together with har, which is how Danish forms the present perfect.

Because roligt is the adverb form here: calmly.

• rolig = calm (adjective)
• roligt = calmly / in a calm way (adverbial use)

In the sentence, it describes how the talking happened:

• vi har talt roligt = we have talked calmly

A useful comparison:

• en rolig person = a calm person
• han taler roligt = he speaks calmly

Neither directly. It describes the verb har talt.

So it tells you the manner of the action:

• vi har talt roligt = we have talked calmly

It does not mean:

• that we are calm people in general
• that the problem is calm

It only tells you how the conversation was carried out.

Because the verb expression is at tale om noget = to talk about something.

So:

• tale om problemet = talk about the problem

You cannot normally drop om here in standard Danish. The preposition belongs with the verb.

Similar examples:

• Vi taler om arbejdet = We talk about work
• De talte om sagen = They talked about the case

Because efter at introduces a subordinate clause.

The basic order in that clause is:

• vi = subject
• har talt = verb phrase

So:

• efter at vi har talt roligt om problemet

This is normal Danish subordinate-clause structure.

A learner may notice that Danish main clauses often have verb-second word order, but after a conjunction like efter at, you are inside a subordinate clause, so the structure is different from a normal independent statement.

Because efter at vi har talt roligt om problemet is a subordinate clause, and Danish often places a comma before such clauses.

So the comma separates:

• main clause: Jeg forstår holdningen bedre
• subordinate clause: efter at vi har talt roligt om problemet

This kind of comma is very common in written Danish.

Yes. Danish allows that very naturally:

• Efter at vi har talt roligt om problemet, forstår jeg holdningen bedre.

That means the same thing.

When the subordinate clause comes first, the main clause shows normal Danish inversion:

• forstår jeg not
• jeg forstår

That is because Danish main clauses keep the finite verb in second position.

Usually both, depending on context.

• at tale can mean to speak
• it can also mean to talk

In this sentence, har talt roligt om problemet is most naturally have talked calmly about the problem.

If the focus were more on language or speaking ability, speak might fit better in another context. But here talked is the best match.

No. In English, you would normally just say after we have talked or more naturally after we talked / after talking depending on context.

In Danish, efter at is the normal pattern here, but in English you do not usually keep the extra that.

So:

• efter at vi har talt = after we have talked not
• after that we have talked

It breaks down like this:

• Jeg = I
• forstår = understand
• holdningen = the attitude / opinion / stance
• bedre = better
• efter at = after
• vi = we
• har talt = have talked
• roligt = calmly
• om problemet = about the problem

So the pattern is:

main clause + subordinate time clause

More specifically:

• Jeg forstår holdningen bedre
  main statement

• efter at vi har talt roligt om problemet
  tells you when or under what prior circumstance that better understanding happened