Daí, eu entendi o problema.

In this sentence, daí is a discourse marker, not the literal from there meaning.

Here it works more like:

• then
• so
• and then
• that’s when

It helps move the story forward. So it sounds like one event led to another, and then the speaker understood the problem.

It can, in other contexts.

For example:

• Eu vim daí. = I came from there.

But in Daí, eu entendi o problema, that is not the meaning. Here daí is being used in a conversational, narrative way to connect ideas.

Because daí is being used as an introductory connector at the start of the sentence.

In writing, a comma is very common:

• Daí, eu entendi o problema.

In informal writing, people may also leave it out:

• Daí eu entendi o problema.

Both are understandable, but the comma is a normal choice when daí introduces the next step in a story.

Yes, you absolutely could.

Portuguese often drops subject pronouns when the verb already makes the subject clear. Since entendi clearly means I understood, eu is not required.

So both are natural:

• Daí, eu entendi o problema.
• Daí, entendi o problema.

Including eu can add:

• a little emphasis
• clarity
• a more explicit spoken rhythm

Entendi is the pretérito perfeito of entender.

That is the normal simple past form used for a completed action. It suggests a specific moment when understanding happened.

So entendi means something like:

• I understood
• I got it
• I realized

It points to the moment the speaker came to understand the problem.

Because entendia is a different past tense: the imperfect.

Compare them:

• entendi = I understood / I got it at that moment
• entendia = I was understanding / I used to understand / I understood in an ongoing background sense

In this sentence, the idea is a clear moment of realization, so entendi is the natural choice.

Portuguese often uses the definite article more than English does.

If the speaker is talking about a specific problem already known in the conversation, o problema is the most natural form.

So:

• entendi o problema = I understood the problem

Saying just entendi problema would sound unnatural in standard Portuguese.

Because not all nouns ending in -a are feminine.

Problema is masculine:

• o problema

This is part of a group of words, many of Greek origin, that end in -ma and are masculine, such as:

• o sistema
• o tema
• o programa

So this is a vocabulary pattern you just have to learn.

Often yes, but the tone changes a bit.

• Daí, eu entendi o problema.
• Então, eu entendi o problema.

Both can work as then/so.

The difference is mostly nuance:

• daí sounds very conversational and story-like
• então is more neutral and widely usable

In everyday Brazilian Portuguese, daí is very common in speech when telling what happened next.

Yes, very often.

• Aí, eu entendi o problema.
• Daí, eu entendi o problema.

Both are common in spoken Brazilian Portuguese.

Very roughly:

• aí is extremely common for then/and then
• daí can sound a bit more like so/then/from that point

In many real conversations, the difference is small, and both can sound natural.

Roughly like dah-EE.

Important points:

• it has two syllables
• the stress is on the second syllable
• the accent mark on í shows that stress

So it is pronounced approximately:

• da-Í

not like a single-syllable English word.

Not with this same meaning.

If daí means then/so as a discourse connector, it is most natural at the beginning:

• Daí, eu entendi o problema.

If you say:

• Eu entendi o problema daí

that will usually sound like I understood the problem from there/from that, which is a different meaning.

So for the narrative then/so meaning, keep daí near the beginning.

It is natural and common, but somewhat informal because of daí.

The rest of the sentence is completely standard:

• eu entendi o problema

What makes it more conversational is the connector daí. In more formal writing, someone might choose a different connector or none at all.