Después de debatir un rato, conseguimos ponernos de acuerdo y aclarar qué idea queríamos destacar en la presentación.

Because in Spanish, después de + infinitive is a very common way to say after doing something when the subject is the same.

• Después de debatir un rato... = After debating for a while...
• It is compact and very natural.

You could also say:

• Después de que debatimos...
• Después de que debatimos un rato...

But that structure is less natural here and would usually need a finite verb clause for a different emphasis or context. In this sentence, después de + infinitive is the most idiomatic choice.

Un rato means for a while or for some time.

So:

• debatir un rato = to debate for a while

It is a very common everyday expression in Spanish. It does not give an exact amount of time; it just means some time.

You will often see similar phrases:

• hablar un rato = talk for a while
• esperar un rato = wait a while
• descansar un rato = rest for a bit

Conseguir + infinitive often means to manage to do something, to succeed in doing something, or to achieve something after some effort.

Here:

• conseguimos ponernos de acuerdo = we managed to come to an agreement
• conseguimos ... aclarar = we managed to clarify

It suggests that agreement was not immediate; there was some difficulty first.

Compared with other verbs:

• pudimos focuses more on being able to
• logramos is similar to conseguimos, but can sound a bit more formal or result-focused
• conseguimos often feels very natural in everyday Spanish

Ponerse de acuerdo is a fixed expression meaning:

• to agree
• to come to an agreement
• to get on the same page

So:

• nos pusimos de acuerdo = we agreed / we reached an agreement
• queremos ponernos de acuerdo = we want to come to an agreement

It is reflexive in form, even though in English we do not usually translate it reflexively.

Because Spanish object/reflexive pronouns attach to an infinitive.

The basic verb is:

• ponerse de acuerdo

With nos, it becomes:

• ponernos de acuerdo = for us to agree / to come to an agreement

After a conjugated verb like conseguimos, Spanish allows the pronoun to stay attached to the infinitive:

• conseguimos ponernos de acuerdo

You could not say conseguimos nos poner de acuerdo. That is ungrammatical.

Yes. The verb conseguimos governs both infinitives:

• conseguimos ponernos de acuerdo
• y (conseguimos) aclarar qué idea queríamos destacar

Spanish often avoids repeating the same verb when it clearly applies to both parts.

So the structure is:

• After debating for a while, we managed [to agree] and [to clarify...]

Because here qué introduces an indirect question:

• qué idea queríamos destacar = which idea we wanted to highlight

Even though this is not a direct question with question marks, it is still interrogative in meaning, so qué keeps the accent.

Compare:

• No sé qué quiere = I do not know what he wants
• Decidimos qué idea usar = We decided which idea to use

Without the accent, que usually has other functions, such as that:

• Dijo que vendría = He said that he would come

Queríamos is the imperfect tense of querer.

Here it fits because the sentence is referring to an intention or goal that existed during that discussion process:

• qué idea queríamos destacar = which idea we wanted to highlight

Why not the others?

• queremos would mean we want, present tense, so it would not match the past context.
• quisimos is preterite, which often sounds more like we tried to / we intended to at a specific moment, not the ongoing shared intention in that discussion.

The imperfect is very natural for describing:

• ongoing mental states
• intentions
• background context in the past

In this sentence, debatir suggests discussing or debating ideas.

• debatir = to debate, discuss in an analytical or structured way
• discutir can mean to argue as well as to discuss

So debatir is a good choice because the context is about exchanging viewpoints in order to decide something for a presentation. It sounds more neutral and collaborative than discutir, which can sometimes suggest conflict.

Here aclarar means to make clear, to clarify, or to sort out.

So:

• aclarar qué idea queríamos destacar = to clarify which idea we wanted to highlight

It implies that the group removed confusion and defined the message more clearly.

Common uses of aclarar:

• aclarar una duda = clarify a doubt / clear up a question
• aclarar un problema = sort out a problem
• aclarar una idea = make an idea clearer

Destacar here means to highlight, to emphasize, or to make stand out.

In a presentation, destacar una idea means choosing the main point you want your audience to notice most.

It is a very common verb in academic, professional, and presentation contexts.

Examples:

• Queremos destacar los puntos principales = We want to highlight the main points
• El informe destaca la importancia del cambio = The report highlights the importance of change

Because qué already works as a determiner here, meaning what or which.

So:

• qué idea = what idea / which idea

You would not say la qué idea.

This is the same pattern as:

• No sé qué libro comprar = I do not know which book to buy
• Decidimos qué camino tomar = We decided which path to take

Because Después de debatir un rato is an introductory phrase.

In writing, Spanish often places a comma after this kind of opening element to separate it from the main clause:

• Después de debatir un rato, conseguimos...

It helps readability and sounds natural in formal and neutral writing.

In very short sentences, commas can sometimes be omitted, but here the comma is standard and appropriate.

Yes, depending on context, English may translate it as:

• in the presentation
• for the presentation

Literally, en la presentación means in the presentation, but natural English sometimes prefers for the presentation if the focus is preparation.

For example:

• qué idea queríamos destacar en la presentación
  • literally: which idea we wanted to highlight in the presentation
  • naturally in context: which idea we wanted to highlight for the presentation

Both can work in English, even though Spanish uses en.

Yes. Logramos would also be correct:

• Después de debatir un rato, logramos ponernos de acuerdo...

Both lograr and conseguir can mean to manage to or to succeed in.

Very roughly:

• conseguir often feels slightly more everyday
• lograr can feel a little more formal or more focused on the achievement itself

But in this sentence, either would sound natural.