Depois de ter caminhado no parque, reparei numa mancha de relva nas calças.

Both are possible, but they are not exactly the same in feel.

• depois de caminhar = after walking
• depois de ter caminhado = after having walked

The version with ter + past participle emphasizes that the walking was already completed before the next action happened. It is a very natural way to show sequence clearly.

So in this sentence, depois de ter caminhado no parque highlights that the walk happened first, and only then did the speaker notice the stain.

It is the perfect infinitive.

It is formed with:

• ter = the infinitive of to have
• caminhado = past participle of caminhar

So:

• ter caminhado = to have walked

After expressions like depois de, Portuguese often uses this structure to show that one action was completed before another.

Numa is a contraction of:

• em
  • uma = numa

This happens because the verb reparar, when it means to notice, normally takes the preposition em:

• reparar em algo = to notice something

So:

• reparei em uma mancha becomes
• reparei numa mancha

This contraction is very common and natural in Portuguese.

Because reparar em is the standard pattern when reparar means to notice.

Examples:

• Reparei no erro. = I noticed the mistake.
• Ela reparou na camisa. = She noticed the shirt.

This is important because reparar without em can mean to repair or to fix in some contexts.

So:

• reparar em = to notice
• reparar = to repair/fix

Here it means I noticed, because it appears in the structure reparar em.

That is why reparei numa mancha means noticing a stain, not repairing one.

This is a very useful distinction for learners:

• Reparei no problema. = I noticed the problem.
• Reparei o carro. = I repaired the car.

Literally, mancha de relva is something like a stain of grass.

In Portuguese, de often links a noun to the material, source, or type of something:

• mancha de vinho = wine stain
• mancha de tinta = ink stain
• mancha de relva = grass stain

So de here tells you what kind of stain it is.

Yes. In European Portuguese, relva is a very normal word for grass, especially lawn grass or grass in a park or garden.

That makes mancha de relva a very natural expression in Portugal.

A learner may also see other words in other varieties or contexts, but for Portugal, relva fits very well here.

Because calças is normally plural in Portuguese, just like trousers in British English.

So:

• as calças = the trousers / the pants
• nas calças = em + as calças

That gives:

• em + as = nas

So nas calças means on/in the trousers/pants.

Portuguese often leaves out possessives when the meaning is already obvious from context.

So if the speaker is talking about their own clothes, nas calças is often enough. You do not need to say nas minhas calças unless you want to be extra specific or emphatic.

Both are possible:

• nas calças = on the trousers/pants
• nas minhas calças = on my trousers/pants

The shorter version is very common.

Because no parque expresses location: the action happened in the park.

• no parque = em + o parque = in the park

By contrast, ao parque usually suggests movement to the park, especially with a verb of motion:

• Fui ao parque. = I went to the park.

But here the sentence is about walking in the park, so no parque is the natural choice.

Because Portuguese often omits subject pronouns when the verb ending already makes the subject clear.

Here:

• reparei clearly shows I noticed

The ending -ei tells you it is first person singular in the past.

So eu is unnecessary unless you want emphasis or contrast.

Yes, you could.

• Depois de ter caminhado no parque = more neutral, more natural in many situations
• Depois de eu ter caminhado no parque = more explicit

Adding eu can be useful if you want to stress who did the walking, especially if there could be confusion about the subject.

But in this sentence, since the subject is obvious, leaving it out is the most natural choice.

Yes, andar is possible in some contexts, but caminhar is often a better match for to walk in the sense of taking a walk or walking for a while.

• caminhar = to walk
• andar = to walk / to go around / to move / to be / to function, depending on context

Because andar has many meanings, caminhar can sound more precise here. In a sentence about spending time walking in a park, caminhar is very natural.

Yes. A very common simpler version would be:

• Depois de caminhar no parque, reparei numa mancha de relva nas calças.

This is also natural and correct.

The original version with ter caminhado is just a bit more explicit about the walking being completed before the noticing happened.