Nia teamo komencos la projekton post la kunveno.

-os is the Esperanto ending for the future tense. So komencos means will begin / will start.

• komencas = begins / is beginning
• komencis = began
• komencos = will begin

So Nia teamo komencos... means Our team will begin...

The -n ending marks the direct object in Esperanto. The direct object is the thing directly affected by the verb.

Here:

• Nia teamo = the subject (the doer)
• komencos = will begin
• la projekton = the direct object (the thing being begun)

So projekton has -n because the team will begin the project.

la is the definite article, meaning the.

So:

• projekton = a project / project
• la projekton = the project

It is used here because the sentence is talking about a specific project, not just any project.

A useful point: la never changes form in Esperanto. It stays la whether the noun is singular, plural, or accusative.

Because post is a preposition, and the noun after it normally does not take the accusative -n.

So:

• post la kunveno = after the meeting

Here la kunveno is the object of the preposition post, not the direct object of the verb.

Only la projekton gets -n, because it is the direct object of komencos.

post means after.

It is a preposition used to show time or sequence:

• post la kunveno = after the meeting
• post la tagmanĝo = after lunch
• post tri tagoj = after three days

In this sentence, it tells us when the team will begin the project.

nia means our.

In Esperanto, possessive words like mia (my), via (your), lia (his), ŝia (her), nia (our), ilia (their) usually replace la.

So Esperanto normally says:

• nia teamo = our team

not:

• la nia teamo

That second version is not the normal way to say it.

Yes. Possessive words in Esperanto behave like adjectives, so they can agree in number and case with the noun.

Here the noun is:

• singular
• not accusative

So we get:

• nia teamo = our team

If the noun were plural, you would have:

• niaj teamoj = our teams

If it were accusative plural:

• niajn teamojn

In this sentence, simple nia is correct.

Yes, Esperanto word order is fairly flexible because endings help show the grammatical roles.

The most neutral order is:

• Nia teamo komencos la projekton post la kunveno.

But other orders are possible, for example:

• Post la kunveno nia teamo komencos la projekton.

That version puts more emphasis on after the meeting.

Because projekton has the -n ending, it is still clearly the object even if word order changes.

Yes. komenci can be used transitively, meaning it can take a direct object.

So:

• komenci la projekton = to begin the project

That is why la projekton appears as the object.

You may also see intransitive-style uses in some contexts, but in this sentence it clearly means to begin something.

Yes. teamo is a normal Esperanto noun meaning team.

Like most Esperanto nouns, it ends in -o:

• teamo = team
• projekto = project
• kunveno = meeting

This -o ending is one of the most basic and regular features of Esperanto nouns.

A rough English-friendly pronunciation is:

NEE-ah teh-AH-moh koh-men-TSOHSS lah proh-YEK-tohn post lah koon-VEH-noh

A few helpful points:

• c is pronounced like ts
• j is pronounced like English y
• stress is usually on the second-to-last syllable

So:

• teamo → te-A-mo
• komencos → ko-men-COS
• projekton → pro-JEK-ton
• kunveno → kun-VE-no

Sometimes yes, but it changes the nuance slightly.

• komencos = will begin / will start
• ekkomencos = will start up / will begin suddenly or at the outset

The prefix ek- often emphasizes the beginning of an action. In many situations, plain komencos is the more neutral and natural choice.

So in this sentence, komencos is perfectly good and probably the most straightforward option.