Learn Hardcore Portuguese (Brazil): Eu gostei da sua resposta na última reunião online. - I liked your answer in the last online meeting.

Gostei is the past tense (pretérito perfeito) of gostar, meaning I liked (a specific event in the past).
Gosto is the present tense, meaning I like (in general, now).

Eu gostei da sua resposta na última reunião online.
→ I liked your answer in that particular meeting.
Eu gosto da sua resposta.
→ I like your answer (as an opinion now, not tied to a past event).

Because you’re talking about something that happened in the last online meeting, the past tense gostei is the natural choice.

Why is it gostei da sua resposta and not just gostei sua resposta?

In Portuguese, gostar almost always needs the preposition de before the thing you like.

Structure:
gostar de + [thing/person]

Eu gosto de café. – I like coffee.
Ela gosta do filme. – She likes the movie.

In your sentence:

gostei de + a sua resposta
de + a contracts to da, so you get:
gostei da sua resposta

You cannot say gostei sua resposta; it sounds wrong to native speakers. You must have de (often in a contraction like do/da/dos/das):

Gostei da sua resposta. ✓
Gostei de sua resposta. ✓ (less common in Brazil, but correct)
Gostei sua resposta. ✗

What exactly is da in da sua resposta?

Da is a contraction of:

de + a = da

Here:

gostar de (to like) requires de
a resposta (the answer) uses the feminine article a

So we have:

gostei de a resposta → grammatically must contract → gostei da resposta

With the possessive:

gostei de a sua resposta → gostei da sua resposta

Similar contractions:

de + o = do → Eu gostei do filme.
de + os = dos → Eu gostei dos comentários.
de + as = das → Eu gostei das ideias.

Why is there an article before the possessive: da sua resposta and not just de sua resposta?

In Brazilian Portuguese, it is very common to use the definite article with a possessive:

a sua resposta (literally: the your answer)
a minha casa (the my house)
o nosso plano (the our plan)

So:

gostei da sua resposta
(de + a sua resposta)

You can say de sua resposta without the article, and it is grammatically correct, but it sounds more formal, sometimes more written than spoken, and less natural in everyday Brazilian speech.

Typical Brazilian preference:

Gostei da sua resposta. ✓ (most natural)
Gostei de sua resposta. ✓ (correct, but less colloquial)

What does sua mean here? Is it your, his, or her answer?

Sua (and seu) are ambiguous in Portuguese; they can mean:

your (when speaking to você)
his
her
sometimes their

In everyday Brazilian Portuguese, context usually tells you the meaning. In your sentence, we’d normally interpret sua as your (talking to você):

Eu gostei da sua resposta na última reunião online.
→ I liked your answer in the last online meeting.

If you need to avoid ambiguity, you can be more explicit:

Eu gostei da resposta dele. – I liked his answer.
Eu gostei da resposta dela. – I liked her answer.
Eu gostei da sua resposta, João. – I liked your answer, João. (now it’s clear from the name)

What’s the difference between sua and seu, and when do I use each one?

Seu/sua agree in gender and number with the thing possessed, not with the owner.

Masculine singular: seu
Feminine singular: sua
Masculine plural: seus
Feminine plural: suas

Examples:

seu livro – your/his/her book (livro = masc.)
sua resposta – your/his/her answer (resposta = fem.)
seus computadores – your/his/her computers
suas ideias – your/his/her ideas

So in sua resposta, we choose sua because resposta is feminine.

Why is it na última reunião online and not em a última reunião online?

Na is another contraction:

em + a = na

You could write it separated in theory (em a), but in real Portuguese it must contract:

em + o = no → no escritório (in the office)
em + a = na → na reunião (in the meeting)
em + os = nos → nos carros (in the cars)
em + as = nas → nas casas (in the houses)

So:

em a última reunião online → na última reunião online

Using em a without contracting sounds wrong.

Why is última feminine here?

Adjectives in Portuguese must agree with the gender and number of the noun they describe.

reunião (meeting) is feminine singular.
So último (last) has to become última to match.

Examples:

o último dia – the last day (masc. sing.)
a última reunião – the last meeting (fem. sing.)
os últimos dias – the last days (masc. plural)
as últimas reuniões – the last meetings (fem. plural)

In your sentence:

na última reunião online
→ reunião is feminine, so última is feminine.

Can I drop Eu and just say Gostei da sua resposta na última reunião online?

Yes. Subject pronouns (eu, você, ele, etc.) are often omitted in Portuguese because the verb ending already shows the person.

Eu gostei da sua resposta.
Gostei da sua resposta.

Both are correct. The version without eu sounds very natural and is actually more common in speech.

You would keep Eu for emphasis or contrast:

Eu gostei da sua resposta, mas eles não gostaram.
I liked your answer, but they didn’t.

Could I say Eu gostava da sua resposta instead of Eu gostei da sua resposta?

It would sound strange. Gostava is the imperfect past, which describes a habit or a continuous state in the past, not a specific event.

Eu gostei da sua resposta.
→ I liked your answer (in that particular situation/meeting).
Eu gostava da sua resposta.
Literally: I used to like your answer / I would like your answer (repeatedly over time).
This doesn’t fit well with a single meeting.

You might say Eu gostava das suas respostas if you mean you generally liked their answers over a period of time:

Eu gostava das suas respostas nas reuniões semanais.
I used to like your answers in the weekly meetings.

Where can I put online? Is na última reunião online the only correct order?

For this sentence, na última reunião online is the most natural and common order:

[na] [última] [reunião] [online]
- preposition + article (na)
- adjective (última)
- noun (reunião)
- descriptor (online)

You would not normally say:

✗ na reunião última online
✗ na online última reunião

Other natural options use a synonym for online:

na última reunião virtual – in the last virtual meeting
na última reunião por videoconferência – via videoconference
na última reunião pela internet – on/over the internet

But the position of última before reunião is stable: última reunião, not reunião última (which sounds poetic or odd in everyday speech).

What’s the difference between na última reunião online and na reunião online passada?

Both can be understood, but they feel slightly different:

na última reunião online
→ the last online meeting (the most recent one, or the final one in a series). This is the most standard and natural way.
na reunião online passada
→ literally in the past online meeting. It’s understandable, but passada (past) here sounds a bit less natural.
More common with semana (week), mês (month), etc.:
- na semana passada – last week
- na reunião da semana passada – in last week’s meeting

So your original version na última reunião online is better and more idiomatic.

How would I make this sentence more obviously formal or polite in Brazilian Portuguese?

Your sentence is neutral and works in most contexts. To be more explicitly polite/formal, Brazilians often:

Add a polite opening:
- Gostaria de dizer que eu gostei da sua resposta na última reunião online.
  I’d like to say that I liked your answer in the last online meeting.
Use titles or names:
- Eu gostei muito da sua resposta na última reunião online, doutor.
- Eu gostei da sua resposta na última reunião online, senhor/senhora.
Use o senhor / a senhora instead of você if you address them directly elsewhere, e.g.:
- Eu gostei da resposta do senhor na última reunião online.
  I liked your answer (sir) in the last online meeting.

But as written, Eu gostei da sua resposta na última reunião online is already perfectly polite in most professional settings.