Depois de lavar a louça, eu gosto de enxugar os pratos logo.

Because depois de is commonly followed by the infinitive when you mean after doing something.

So:

• depois de lavar a louça = after washing the dishes
• literally: after washing the dishes

This is a very common Portuguese pattern:

• depois de comer = after eating
• depois de estudar = after studying
• depois de chegar = after arriving

If you use a conjugated verb instead, you usually need a different structure, such as:

• depois que eu lavo a louça...
• depois que eu lavar a louça...

Those are possible, but they are different constructions. In your sentence, depois de + infinitive is the most natural compact form.

In Portuguese, louça is often used as a collective noun meaning dishes/tableware. Even though it refers to many items, it is grammatically singular here:

• lavar a louça = to wash the dishes

This is very natural in Brazilian Portuguese. English does something similar with words like furniture or luggage: grammatically singular, but referring to multiple things.

So even though louça includes many objects, you still say:

• a louça
• not necessarily as louças

Because louça is broad, while pratos is specific.

• a louça = the dishes / tableware in general
• os pratos = the plates

So the sentence means something like:

• After washing the dishes, I like to dry the plates right away.

This can sound a little more specific than the first part. In real life, speakers do this kind of shift naturally. Maybe the speaker means that after washing everything, the plates are the items they especially like to dry immediately.

If you wanted, you could also say:

• Depois de lavar a louça, eu gosto de enxugar a louça logo.

But that sounds a bit repetitive.

No, eu is not strictly necessary here.

Portuguese often allows the subject pronoun to be omitted because the verb ending already shows the subject:

• eu gosto
• gosto

Both can mean I like.

So these are both natural:

• Depois de lavar a louça, eu gosto de enxugar os pratos logo.
• Depois de lavar a louça, gosto de enxugar os pratos logo.

Including eu can add:

• emphasis
• clarity
• a slightly more explicit style

Brazilian Portuguese uses subject pronouns more often than European Portuguese, but omission is still very common.

Because gostar normally requires the preposition de.

So:

• gostar de + noun
• gostar de + infinitive

Examples:

• gosto de café = I like coffee
• gosto de estudar = I like to study
• gosto de enxugar os pratos = I like drying the plates / I like to dry the plates

This is just how the verb works in Portuguese. You cannot normally say gosto enxugar.

Both can relate to drying, but they are not always identical.

In this sentence, enxugar usually suggests wiping something dry, often with a cloth or towel.

• enxugar os pratos = dry/wipe the plates dry

Secar is more general:

• to dry
• to become dry
• to dry something

Examples:

• Vou secar a roupa. = I’m going to dry the clothes.
• O chão secou. = The floor dried.
• Vou enxugar os pratos. = I’m going to dry the plates by wiping them.

For dishes, enxugar is very natural when you mean towel-drying them.

Here, logo means something like:

• right away
• soon
• immediately afterward

So:

• enxugar os pratos logo = dry the plates right away

In Brazilian Portuguese, logo often gives the idea of doing something without much delay.

Examples:

• Volto logo. = I’ll be back soon.
• Faz isso logo. = Do that now / Hurry up and do that.

In your sentence, it suggests that the speaker likes to dry the plates soon after washing them, rather than leaving them there.

Yes. Portuguese often allows some flexibility with adverbs like logo.

These are all possible, depending on emphasis and style:

• eu gosto de enxugar os pratos logo
• eu gosto logo de enxugar os pratos
• logo depois de lavar a louça, eu gosto de enxugar os pratos

But the original version is very natural. In that position, logo most clearly modifies the action of drying the plates: right away.

Because depois de lavar a louça is an introductory phrase, and Portuguese commonly uses a comma after that kind of opening element.

So:

• Depois de lavar a louça, eu gosto de enxugar os pratos logo.

This comma helps separate the introductory idea from the main clause.

In informal writing, people sometimes leave out commas, but in standard writing this comma is a good choice.

Yes, but it is a different structure.

Compare:

• Depois de lavar a louça... = after washing the dishes
• Depois que eu lavo a louça... = after I wash the dishes / after I do the dishes

The original sentence uses the infinitive structure, which is shorter and very natural.

If you say:

• Depois que eu lavo a louça, eu gosto de enxugar os pratos logo.

it sounds more explicit because it states the subject and conjugates the verb. It is not wrong, just less compact.

Usually, yes. The most natural interpretation is that the same person does both actions:

• after washing the dishes, I like to dry the plates right away

Because there is no new subject introduced in the first part, listeners normally connect it to eu in the main clause.

If you wanted to make a different subject clear, you would usually say so explicitly.

Yes, very much so. Lavar a louça is the normal everyday expression for:

• to wash the dishes
• to do the dishes

It is one of the most common household phrases in Portuguese.

Examples:

• Tenho que lavar a louça. = I have to wash the dishes.
• Você lavou a louça? = Did you wash the dishes?

So this is a phrase worth learning as a chunk.

Yes. In English, those two versions are very close, and Portuguese does not make a sharp distinction here.

• gosto de enxugar os pratos can mean:
  • I like drying the plates
  • I like to dry the plates

The Portuguese structure is simply:

• gostar de + infinitive

The exact English translation depends on what sounds most natural in context.

A rough guide:

• louça ≈ LOH-sa
• enxugar ≈ en-shoo-GAR or ẽ-shoo-GAR, depending on accent

A few useful details:

• the ç in louça sounds like s
• ou in louça sounds somewhat like the o sound in go, but not exactly the same in every accent
• x in enxugar sounds like sh
• the final r in Brazilian Portuguese is often softer than an English r, and in many accents it can sound almost like h

You do not need perfect pronunciation right away, but it helps to know that enxugar begins with an en-sh sound, not an English ex sound.

Yes, it sounds natural. It is a normal kind of everyday sentence.

The only small thing to notice is that some speakers might choose slightly different wording depending on habit, for example:

• Depois de lavar a louça, gosto de secar os pratos logo.
• Depois de lavar a louça, eu gosto de enxugar tudo logo.

But the original sentence is completely natural and understandable in Brazilian Portuguese.