Eu quero entender o motivo do atraso.

Yes, you usually can leave it out in Portuguese.

Eu quero entender o motivo do atraso.
and
Quero entender o motivo do atraso.

both mean the same thing in most situations.

Portuguese often drops subject pronouns because the verb form already shows who the subject is. Quero clearly means I want.

You might keep Eu when:

• you want to add emphasis
• you want to make a contrast

For example:

• Eu quero entender, mas ele não.
  I want to understand, but he doesn’t.

So in everyday speech, Quero entender o motivo do atraso is very natural.

After querer when it means to want to do something, Portuguese uses the infinitive of the second verb.

So:

• quero entender = I want to understand
• quero comer = I want to eat
• quero sair = I want to leave/go out

This is similar to English want to + verb.

Entendendo is the gerund, like understanding, and it would not fit here.

In this sentence, entender means to understand.

It is very close to compreender, and in many cases they are interchangeable:

• Quero entender o motivo do atraso.
• Quero compreender o motivo do atraso.

Both are correct.

That said:

• entender is often more common in everyday speech
• compreender can sound a little more formal or more complete/deeper, depending on context

For most learners, entender is the more useful everyday choice.

Portuguese often uses the definite article where English may not.

So o motivo literally means the reason or the motive.

In this sentence, o motivo do atraso means:

• the reason for the delay
• more literally, the reason of the delay

Using o here is completely natural.
Saying just motivo would sound incomplete or unnatural in this sentence.

Because do is a contraction:

• de + o = do

So:

• o motivo do atraso literally = the reason of the delay

In natural English, we usually say:

• the reason for the delay

Portuguese often uses de in places where English uses for or of, so it is better not to translate word-for-word too rigidly.

A few similar examples:

• a causa do problema = the cause of the problem
• o fim do filme = the end of the movie
• o nome do professor = the teacher’s name / the name of the teacher

Here, atraso means delay.

It can refer to:

• a person being late
• an event starting late
• something arriving late
• a general delay in a process

Examples:

• O voo teve atraso. = The flight had a delay.
• Desculpe o atraso. = Sorry for the delay.
• Ele está com atraso. = He is running late.

So o motivo do atraso is a very common and natural way to say the reason for the delay.

All three can relate to reason, but they are not always used in exactly the same way.

motivo

A very common word for reason in many situations.

• Quero entender o motivo do atraso.

razão

Also means reason, and can sound slightly more formal or abstract in some contexts.

• Quero entender a razão do atraso.

causa

Usually means cause, often when you want to focus on what produced the result.

• Quero entender a causa do atraso.

In this sentence:

• motivo sounds very natural
• razão is also possible
• causa may sound a bit more analytical or technical, depending on context

Not in the same structure.

You can say:

• Quero entender o motivo do atraso.
• Quero entender por que houve atraso.
• Quero entender por que está atrasado.

But por que introduces a clause, not a noun phrase.

Compare:

Noun phrase

• o motivo do atraso = the reason for the delay

Clause

• por que houve atraso = why there was a delay

So both are correct, but the grammar is different.

It sounds neutral to slightly formal, but still very natural.

Why?

• quero entender sounds polite and controlled
• o motivo do atraso is a bit more structured than a very casual version

A more casual version might be:

• Quero entender por que atrasou.
• Queria saber o motivo do atraso.
• O que aconteceu com o atraso? (less direct equivalent depending on context)

A more formal version might be:

• Gostaria de entender o motivo do atraso.

So the original sentence works well in many situations, especially when speaking politely.

Usually not in this exact meaning.

O motivo do atraso means the reason for the delay, referring to a specific delay.

Motivo de atraso is possible in some contexts, but it sounds more general, like:

• a cause of delay
• a reason that something may be delayed

Compare:

• Quero entender o motivo do atraso. = I want to understand the reason for the delay.
• Chuva é um motivo de atraso em aeroportos. = Rain is a cause of delay in airports.

So for the sentence you have, do atraso is the natural choice.

A rough pronunciation guide is:

eh-ooh KEH-roh en-ten-DER oo moh-CHEE-voo doo ah-TRAH-zoo

A few helpful notes:

• Eu often sounds like eh-ooh said quickly
• quero has an open e sound in Brazilian Portuguese
• entender has stress on the last syllable: -der
• motivo has stress on ti
• atraso has stress on tra

In natural speech, it may flow together more like: Eu quero entendêro motivo do atraso

That linking between words is normal.

Yes.

• Eu quero entender o motivo do atraso. = I want to understand the reason for the delay.
• Eu queria entender o motivo do atraso. = I wanted to understand / I’d like to understand the reason for the delay.

In real use, queria often sounds softer, more polite, less direct than quero, even though it is past imperfect in form.

So:

• quero = more direct, straightforward
• queria = more tactful, more polite

This is very common in Portuguese, especially when making requests or expressing something delicately.

A little, but the original order is the most natural.

Standard order:

• Eu quero entender o motivo do atraso.

You could also say:

• Quero entender o motivo do atraso.
• O motivo do atraso eu quero entender. (marked/emphatic)
• Eu quero o motivo do atraso entender. (incorrect)

So the normal pattern is:

subject + querer + infinitive + object

Here:

• Eu = subject
• quero = main verb
• entender = infinitive
• o motivo do atraso = object

For learners, it is best to stick with the original order unless you specifically want emphasis.