A mi hija le gusta mirar el castillo de lejos desde el mirador.

Because gustar works differently from to like in English.

In Spanish, gustar literally works more like to be pleasing to. So:

• A mi hija = to my daughter
• le = to her
• gusta = is pleasing
• mirar el castillo... = watching/looking at the castle...

So the structure is basically:

Watching the castle from afar from the viewpoint is pleasing to my daughter.

That is why mi hija is not the grammatical subject here. The thing being liked is the subject, and mi hija is the person receiving that feeling.

Yes, they both point to the same person, but this is very normal in Spanish.

This is called clitic doubling. In sentences with gustar and similar verbs, Spanish often uses:

• the indirect object pronoun: le
• plus the fuller phrase: a mi hija

So:

• le gusta = she likes it / literally it pleases her
• A mi hija le gusta = My daughter likes it

The fuller phrase A mi hija can:

• clarify who le refers to
• add emphasis
• avoid ambiguity

In many cases, especially with names, people, or for clarity, using both is the most natural option.

Because the grammatical subject is singular.

What is pleasing to her here is the whole action:

mirar el castillo de lejos desde el mirador

An infinitive phrase like mirar... counts as singular, so Spanish uses gusta.

Compare:

• Le gusta mirar el castillo. = She likes looking at the castle.
• Le gustan los castillos. = She likes castles.

In the second sentence, los castillos is plural, so you get gustan.

After gustar, Spanish often uses an infinitive to express an activity someone likes.

So:

• Le gusta mirar = She likes looking / She likes to look
• Le gusta leer = She likes reading / She likes to read
• Le gusta caminar = She likes walking / She likes to walk

The infinitive is the normal way to say doing something after gustar.

Both can relate to sight, but they are not exactly the same.

• ver = to see
• mirar = to look at / to watch

In this sentence, mirar suggests a more deliberate action: she intentionally looks at the castle.

So:

• ver el castillo = to see the castle
• mirar el castillo = to look at the castle

Because the sentence describes the activity she enjoys, mirar is a very natural choice.

De lejos means from far away or from a distance.

It is a fixed expression in Spanish:

• ver algo de lejos = to see something from far away
• mirar algo de lejos = to look at something from a distance

Spanish uses de here, not something like a direct equivalent of farly or distantly. It is just the normal idiomatic expression.

You can think of it as:

• de cerca = from up close
• de lejos = from far away

Because desde means from, indicating the viewing point or origin of the action.

• desde el mirador = from the viewpoint
• en el mirador = at/on the viewpoint

Both can make sense in some contexts, but they are slightly different.

Here, desde el mirador emphasizes the place from which she looks at the castle. It answers the question: From where does she look at it?

Using en el mirador would focus more on her location, while desde el mirador focuses more clearly on the viewpoint as the observation point.

In Spain, mirador usually means a viewpoint, lookout point, or scenic overlook—a place designed for looking out at scenery.

Depending on context, it could be:

• a terrace with a view
• a lookout platform
• a scenic observation point

In this sentence, el mirador is the place from which the castle is viewed.

Starting with A mi hija helps establish right away who experiences the liking.

Spanish often places this kind of phrase near the beginning for clarity or emphasis, especially with gustar. It is a very natural word order.

You could think of it as:

• As for my daughter, she likes looking at the castle...

It is not the only possible order, but it is a common and clear one.

Yes, that is grammatically correct.

Using ver instead of mirar changes the nuance slightly:

• mirar = to look at, more intentional
• ver = to see

So:

• le gusta mirar el castillo = she likes looking at the castle
• le gusta ver el castillo = she likes seeing the castle

Both are possible, but mirar often fits better when the idea is enjoying the act of gazing at it.

In normal use, mi hija means my daughter.

Unlike English, Spanish does not usually need an apostrophe structure like my daughter’s here, because this phrase is not showing possession; it is identifying the person who likes the action.

So in this sentence:

• A mi hija = to my daughter
• not of my daughter
• not my daughter’s

The phrase simply marks who the experience belongs to.