A mi hija le gusta mirar el molino de viento desde la granja.

Because gustar works differently from the English verb to like.

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

• A mi hija le gusta mirar el molino de viento
  = Looking at the windmill is pleasing to my daughter = My daughter likes looking at the windmill

So:

• a mi hija = to my daughter
• le gusta = is pleasing to her

That is why mi hija is not the grammatical subject here. The thing being liked is the subject, not the person who likes it.

Le is the indirect object pronoun, meaning to her here.

So in:

• A mi hija le gusta mirar el molino de viento

both a mi hija and le point to the same person.

This is very common in Spanish. The pronoun is usually kept even when the full phrase is also present.

You can think of it like this:

• a mi hija = clarifies who we mean
• le = the normal pronoun that goes with gustar

So Spanish often uses both:

• A Juan le gusta...
• A mi madre le encanta...
• A nosotros nos gusta...

Because the subject of gustar here is the whole action:

• mirar el molino de viento desde la granja

That whole infinitive phrase counts as a singular idea, so Spanish uses gusta.

Compare:

• Le gusta mirar el molino de viento.
  = She likes looking at the windmill.

But:

• Le gustan los molinos de viento.
  = She likes windmills.

In the second sentence, los molinos de viento is plural, so the verb becomes gustan.

After gustar, Spanish often uses an infinitive to express liking to do something.

So:

• le gusta mirar = she likes to look / she likes looking

This is very common:

• Me gusta leer = I like reading
• Nos gusta viajar = We like travelling
• Les gusta comer fuera = They like eating out

The infinitive in Spanish often covers both English meanings:

• to look
• looking

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

• ver = to see
• mirar = to look at

So in this sentence, mirar suggests actively directing attention at the windmill.

Examples:

• Veo el molino. = I see the windmill.
• Miro el molino. = I look at the windmill.

In many situations, Spanish speakers choose mirar when they mean a deliberate action of looking.

Because the normal Spanish expression is molino de viento, literally mill of wind.

It is a fixed expression:

• molino = mill
• de viento = of wind / wind-powered

So:

• el molino de viento = the windmill

This use of de is very common in Spanish to describe what something is made for, powered by, or associated with.

Spanish uses definite articles more often than English.

Here:

• el molino de viento = the windmill
• la granja = the farm

The article must match the noun’s gender and number:

• molino is masculine singular → el
• granja is feminine singular → la

Even when English might sometimes omit the, Spanish often keeps it.

Desde la granja means from the farm.

In this sentence, it most naturally tells you the viewing position:

• A mi hija le gusta mirar el molino de viento desde la granja.
• My daughter likes to look at the windmill from the farm.

So the idea is that she is at the farm, and from there she looks at the windmill.

It most naturally describes the action of looking, not the windmill itself.

So the meaning is:

• She likes looking at the windmill while being at / from the position of the farm.

Not usually:

• the windmill that comes from the farm

Spanish allows this kind of phrase at the end, and context usually makes the meaning clear.

Because desde means from in the sense of a starting point or viewpoint.

• desde la granja = from the farm

Using just de la granja would usually not mean the same thing here. De has many uses, but it would not normally express this viewing position as clearly.

So:

• mirar el molino desde la granja = look at the windmill from the farm

is the natural choice.

Sometimes yes, but not always with the same effect.

1. Le gusta mirar el molino de viento desde la granja.
   This is grammatical, but le could mean to him, to her, or to you depending on context.

2. A mi hija gusta mirar...
   This sounds wrong. With gustar, the pronoun is normally needed: le gusta.

3. A mi hija le gusta mirar...
   This is the clearest and most natural full version.

So:

• le is normally required
• a mi hija is optional if the context already makes it clear who le refers to

Because Spanish is not trying to copy the English structure My daughter likes...

Instead, Spanish builds the sentence around gustar:

• A mi hija = to my daughter
• le gusta = is pleasing to her
• mirar el molino de viento desde la granja = looking at the windmill from the farm

So the order reflects how gustar works in Spanish, not how to like works in English.

Yes, that is grammatical, but the nuance changes a bit.

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

So:

• le gusta mirar el molino suggests a more deliberate act of looking
• le gusta ver el molino can sound a bit more general, like she enjoys seeing it

In many contexts both are possible, but mirar fits especially well if she intentionally looks at it.

Here it means my daughter.

Breakdown:

• mi = my
• hija = daughter

Also useful to compare:

• hijo = son
• hija = daughter

So mi hija is feminine because it refers to a daughter.