Después de haber tachado muchas palabras de la lista, me siento más tranquilo.

Haber tachado is the perfect infinitive. It literally means to have crossed out.

In this sentence, it shows that the crossing out happened before the feeling in the main clause:

• Después de haber tachado... = After having crossed out...
• me siento más tranquilo = I feel calmer / more at ease

Spanish often uses this structure after expressions like después de when it wants to make it especially clear that one action was completed first.

Yes, absolutely.

Both are possible:

• Después de tachar muchas palabras de la lista...
• Después de haber tachado muchas palabras de la lista...

The version with haber tachado sounds a bit more explicit about the action being completed beforehand. The shorter version, después de tachar, is also very natural and common.

So the difference is mostly one of emphasis and style, not basic meaning.

Because when después is followed by a noun or an infinitive, Spanish normally uses de:

• después de comer
• después de la cena
• después de haber tachado muchas palabras

You can use después by itself when nothing follows it directly:

• Primero trabajé y después descansé.

And before a full clause, Spanish often uses después de que:

• Después de que terminé, descansé.

So in your sentence, de is required because it is followed by haber tachado.

Tachar usually means to cross out, to strike out, or to mark something as done by drawing a line through it.

In the context of a list, it suggests removing items visually, for example by putting a line through them once they are finished or no longer relevant.

In Spain, this is a very common verb for that idea.

It is not quite the same as borrar:

• tachar = cross out
• borrar = erase / delete

So tachado muchas palabras de la lista suggests physically or visually crossing them off the list.

Because palabras is a feminine plural noun.

Spanish adjectives and determiners have to agree with the noun they describe:

• mucho = masculine singular
• mucha = feminine singular
• muchos = masculine plural
• muchas = feminine plural

So:

• muchas palabras = correct
• muchos palabras = incorrect

De la lista tells you which words we are talking about: the words from / on the list.

So:

• muchas palabras = many words
• muchas palabras de la lista = many words from the list / many words on the list

This is a very common way in Spanish to specify what set something belongs to.

Spanish often uses sentirse to talk about how someone feels emotionally or physically.

• Me siento más tranquilo = I feel calmer / more at ease

Using estar would focus more on a state:

• Estoy más tranquilo = I am calmer

Both can be correct in many contexts, but me siento highlights the speaker’s internal feeling more directly. In this sentence, that makes very good sense, because crossing things off a list gives the speaker a feeling of relief.

Here más is comparative: more calm / calmer.

Spanish often leaves the second part unstated when it is obvious from context. So this means something like:

• calmer than before
• calmer than I was earlier
• more at ease now

That comparison does not have to be said explicitly.

Also, tranquilo agrees with the speaker:

• a male speaker: más tranquilo
• a female speaker: más tranquila

Because it describes the speaker, represented by me and understood as yo.

The sentence means:

• I feel calmer

Since it refers to one person, the adjective is singular:

• tranquilo for a male speaker
• tranquila for a female speaker

It is not agreeing with palabras. That noun belongs to the earlier part of the sentence and has nothing to do with the adjective tranquilo.

Yes, it can definitely suggest relieved, more at ease, or less worried, depending on context.

Tranquilo often covers a range of ideas in Spanish, such as:

• calm
• relaxed
• at ease
• reassured
• not worried

In this sentence, because the speaker has crossed many words off a list, more at ease or more relieved is a very natural interpretation.

That opening phrase sets the scene first:

• Después de haber tachado muchas palabras de la lista, ...
• After having crossed out many words on the list, ...

Then the main idea comes:

• me siento más tranquilo
• I feel calmer

This is a very normal Spanish word order. It is similar to English, where you can also begin with the time/action phrase first.

You could also say:

• Me siento más tranquilo después de haber tachado muchas palabras de la lista.

That version is also correct. The difference is mainly one of emphasis. The original sentence puts the earlier action in the foreground first.