После долгого обсуждения мы окончательно договорились о времени встречи.

После means after, but unlike English, it is a preposition that requires the genitive case.

So:

• обсуждение → обсуждения
• долгое → долгого

That is why we get:

• после долгого обсуждения = after a long discussion

This is a very common pattern in Russian:

• после урока = after the lesson
• после работы = after work
• после встречи = after the meeting

Because the whole phrase comes after после, and после requires the genitive.

The base form is:

• долгое обсуждение = a long discussion

But after после, both the adjective and noun must switch to genitive singular:

• долгого = genitive singular of долгий
• обсуждения = genitive singular of обсуждение

So:

• после долгого обсуждения

This is standard adjective-noun agreement: the adjective changes case to match the noun.

Окончательно means something like:

• finally
• definitively
• once and for all

In this sentence, it adds the idea that the agreement was not just reached, but settled for good, with no more uncertainty.

So compared with just:

• мы договорились = we agreed / came to an agreement

the version with окончательно suggests:

• the discussion is over
• the issue has been fully settled
• the decision is final

It is stronger than just finally in some contexts, because it often carries the sense of definitively.

Договорились is:

• past tense
• plural
• from the verb договориться
• perfective
• reflexive (because of -ся)

Breakdown:

• договориться = to come to an agreement / to agree
• договорились = we/they came to an agreement

Why plural? Because the subject is мы.

Why perfective? Because the sentence describes a completed result: after the discussion, the agreement was reached.

Compare:

• договаривались = were negotiating / were trying to agree / used to agree
• договорились = succeeded in agreeing

So договорились focuses on the completed outcome.

The -ся is important here. It is part of the verb договориться, which means:

• to come to an agreement
• to agree with someone
• to settle something by agreement

This is different from договорить, which usually means:

• to finish speaking
• to say something to the end

So:

• договорить = to finish what you are saying
• договориться = to reach an agreement

They are different verbs, even though they look similar.

In this sentence, only договориться makes sense.

Because the verb договориться is commonly used with о + prepositional case when talking about what people agreed on.

Pattern:

• договориться о чём? = to agree on/about what?

So:

• о времени = about/on the time
• о встрече = about the meeting
• о цене = about the price

In this sentence:

• мы договорились о времени встречи
• literally: we agreed on the time of the meeting

This is a standard government pattern of the verb, and it needs to be learned together with the verb.

Because the preposition о here requires the prepositional case.

The noun время changes like this:

• nominative: время
• prepositional: времени

So:

• о времени = about the time

This is one of the nouns with an irregular-looking pattern, so it is worth memorizing:

• время
• времени
• времени
• временем

Russian learners often notice that время does not decline like a regular neuter noun.

Because время встречи means the time of the meeting or meeting time.

Here:

• времени is in the prepositional case because of о
• встречи is in the genitive because it depends on время

The basic phrase is:

• время встречи = the time of the meeting

This is a common noun + noun structure in Russian, where the second noun is often in the genitive to show relationship.

Examples:

• начало фильма = the beginning of the film
• цена билета = the price of the ticket
• план поездки = the plan of the trip

So in the sentence:

• о времени встречи

the whole thing means about the meeting time, and встречи stays in the genitive because it depends on время.

Yes. Russian often drops subject pronouns when they are clear from the verb form.

So this would also be natural:

• После долгого обсуждения окончательно договорились о времени встречи.

Because договорились is plural past tense, the listener can often understand the subject from context.

However, мы may be included:

• for clarity
• for emphasis
• because the speaker wants to explicitly contrast we with someone else

So in this sentence, мы is perfectly normal, but not always strictly necessary.

Yes, Russian word order is flexible.

This sentence starts with:

• После долгого обсуждения

This sets the scene first: after a long discussion.

Then:

• мы окончательно договорились

This gives the main action.

Then:

• о времени встречи

This gives the topic of agreement.

That order is natural because it moves from:

1. background
2. action
3. detail

Other word orders are possible, for example:

• Мы окончательно договорились о времени встречи после долгого обсуждения.
• О времени встречи мы окончательно договорились после долгого обсуждения.

These are grammatically possible, but they shift emphasis.

The original version sounds smooth and neutral, especially in written Russian.

It can overlap with all of those, depending on context.

In this sentence, договорились is probably closest to:

• came to an agreement
• agreed
• settled

Because the phrase is:

• договорились о времени встречи

that means they agreed on the meeting time.

In English, natural translations might include:

• we finally agreed on the meeting time
• we came to a final agreement about the meeting time
• we settled on the time of the meeting

So договориться often emphasizes the idea that people discussed something and then reached a mutually accepted decision.