A mi hija le gusta el puré de patata, pero mi sobrino prefiere la merluza al horno.

Because gustar does not work like English to like.

Spanish structures it more like to be pleasing to:

• el puré de patata = the thing that is pleasing
• a mi hija / le = the person it is pleasing to

So:

• A mi hija le gusta el puré de patata
  literally = Mashed potato is pleasing to my daughter

That is why mi hija is not the subject of gusta.

It marks who likes it: your daughter.

Grammatically, this is the indirect object. It tells us who experiences the liking.

It can also add clarity or emphasis. If you only said:

• Le gusta el puré de patata

it would mean He/She likes mashed potato, depending on context.
Adding a mi hija makes it explicit: my daughter is the one who likes it.

Because in Spanish, with verbs like gustar, the indirect object pronoun is normally still used even when the full phrase is present.

So this pattern is standard:

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

The pronoun and the full phrase often appear together.
So le is not optional here in normal Spanish.

Because the verb agrees with the thing liked, not with the person who likes it.

Here, the thing liked is:

• el puré de patata — singular

So you use:

• gusta

If the thing liked were plural, you would use gustan:

• A mi hija le gustan las croquetas.

Because the two nouns have different jobs in the sentence.

In:

• A mi hija le gusta el puré de patata

mi hija is not the subject. She is the indirect object, so a is used.

In:

• pero mi sobrino prefiere la merluza al horno

mi sobrino is the subject of prefiere, so no a is needed.

So the contrast is:

• a mi hija = indirect object with gustar
• mi sobrino = subject with preferir

Because preferir and gustar behave differently.

Preferir works much more like English to prefer:

• Mi sobrino prefiere la merluza al horno
• subject = mi sobrino
• object = la merluza al horno

But gustar has the reversed-style structure:

• A mi hija le gusta el puré de patata
• subject = el puré de patata
• indirect object = a mi hija / le

This is one of the biggest differences learners notice.

Spanish often uses the definite article with foods, especially in general statements and after verbs like gustar and preferir.

So Spanish says:

• le gusta el puré de patata
• prefiere la merluza al horno

Even though English often drops the article:

• she likes mashed potato
• he prefers baked hake

This is very natural Spanish.

In Spain, puré de patata is very common and natural.

The singular patata is being used as an ingredient/category, a bit like saying potato purée. You may also hear puré de patatas, and that is not wrong, but puré de patata is very normal in Spain.

Also, patata is especially typical of Spain. In many Latin American countries, people often say papa instead.

It means oven-baked hake or hake baked in the oven.

A few useful points:

• merluza = hake
• al = contraction of a + el
• al horno = in the oven / oven-baked

This is a very common cooking expression in Spanish:

• pollo al horno = roast chicken / oven-baked chicken
• patatas al horno = baked potatoes

Preferir is a stem-changing verb in the present tense: e → ie.

So:

• yo prefiero
• tú prefieres
• él/ella prefiere
• nosotros preferimos
• vosotros preferís
• ellos prefieren

That is why the sentence has prefiere and not preferir or prefera.

You can leave out a mi hija if the context already makes it clear who le refers to:

• Le gusta el puré de patata.

But you normally cannot leave out le and keep only a mi hija:

• A mi hija gusta el puré de patata ❌

So:

• A mi hija le gusta... ✅
• Le gusta... ✅
• A mi hija gusta... ❌

Yes, especially for Spain Spanish:

• puré — the accent mark shows the stress is on the last syllable: pu-RÉ
• hija — the j is a strong throaty sound
• horno — the h is silent
• merluza — in most of Spain, z sounds like th in thin
• patata — straightforward pronunciation, with clear vowels

So in Spain, merluza sounds roughly like mer-LU-tha.