Después de trabajar, me gusta desconectar con música en casa.

Because después is normally followed by de in Spanish.

• después de + noun → after + noun
• después de + infinitive → after + -ing / after doing something

So:

• después de trabajar = after working
• después del trabajo = after work

Using trabajar here is very common because after a preposition like de, Spanish often uses the infinitive.

In Spanish, when a verb comes after a preposition and refers to an action in a general way, it usually stays in the infinitive.

Examples:

• antes de salir = before leaving
• sin comer = without eating
• después de trabajar = after working

English often uses -ing in these cases, but Spanish usually uses the infinitive instead.

Because gustar works differently from to like in English.

Spanish structures it more like:

• me gusta X = X is pleasing to me

So in this sentence:

• me = to me
• gusta = is pleasing
• desconectar con música en casa = the thing that is pleasing

That is why Spanish says me gusta rather than yo gusto.

Important:

• yo gusto would usually mean I am pleasing / I am attractive, which is a different idea.

Because the thing being liked is treated as one activity: desconectar con música en casa.

When gustar is followed by an infinitive, it is normally singular:

• Me gusta leer.
• Me gusta viajar.
• Me gusta desconectar con música en casa.

If the thing liked is a plural noun, then you use gustan:

• Me gustan los libros.
• Me gustan las canciones.

Here desconectar does not mean literally to unplug. In Spain especially, it is very commonly used to mean:

• to switch off mentally
• to unwind
• to disconnect from stress
• to zone out / relax

So me gusta desconectar con música means something like:

• I like to unwind with music
• I like to switch off with music

This is a very natural expression in Spanish from Spain.

Because con música is a natural, compact way to express using music as the means of relaxing.

It suggests:

• with music
• by listening to music
• through music

So:

• me gusta desconectar con música = I like to unwind with music

If you said escuchando música, that would also be correct, but it is more explicit:

• Después de trabajar, me gusta desconectar escuchando música.

Both work, but con música sounds very natural and smooth.

Because música is being used in a general sense, not referring to a specific music selection.

Compare:

• con música = with music, in general
• con la música = with the music, a specific music already mentioned or understood

In the sentence, the speaker means music in general, so con música is the normal choice.

En casa is a very common Spanish expression meaning at home.

It does not focus on the physical building so much; it refers to the idea of home as the place where you live.

• en casa = at home
• en la casa = in the house

So in this sentence, en casa is the natural choice because the meaning is at home, not specifically inside the house building.

Me is an indirect object pronoun meaning to me.

In me gusta, it marks who finds something pleasing.

The full idea is:

• A mí me gusta desconectar con música en casa.
• Literally: To me, unwinding with music at home is pleasing.

Often a mí is omitted because me already tells you who the person is.

Other forms are:

• me gusta = I like
• te gusta = you like
• le gusta = he/she/you(formal) likes

Because Después de trabajar is an introductory time phrase, and putting a comma after it is very natural.

• Después de trabajar, me gusta desconectar...

The comma helps separate the time expression from the main part of the sentence. In short everyday writing, you may sometimes see it omitted, but using the comma is clear and standard.

Yes. Both are correct, but they are structured differently:

• Después de trabajar = after working
• Después del trabajo = after work / after the job / after the work

The first focuses on the action. The second uses the noun trabajo.

Both sound natural:

• Después de trabajar, me gusta desconectar con música en casa.
• Después del trabajo, me gusta desconectar con música en casa.

Yes, Spanish word order is fairly flexible, although some versions sound more natural than others.

Original:

• Después de trabajar, me gusta desconectar con música en casa.

Other possible versions:

• Me gusta desconectar con música en casa después de trabajar.
• En casa, me gusta desconectar con música después de trabajar.

The original sounds very natural because it starts with the time context: after working.

Yes. In Spain, desconectar often works perfectly well on its own.

For example:

• Necesito desconectar. = I need to switch off / unwind.
• Los fines de semana me gusta desconectar. = At weekends I like to unwind.

Adding con música just tells you how the person likes to unwind.