Mi hermana prefiere física, pero a mí me gusta más la geografía.

In modern Spanish, possessives like mi, tu, su, nuestro usually replace the article, so you say mi hermana, not la mi hermana.

• mi hermana = my sister
• la hermana = the sister

Using both together is not normal in standard everyday Spanish.

The verb is preferir. In the present tense, it is a stem-changing verb: e → ie in most forms.

So:

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

Since mi hermana is she, the correct form is prefiere.

This is a very common point for learners.

After verbs like preferir, Spanish often leaves out the article when talking about school subjects or general categories:

• prefiere física
• estudio matemáticas
• odio química

But with gustar, Spanish very often uses the definite article with subjects, languages, sports, and other general things:

• me gusta la geografía
• me gustan las matemáticas
• me gusta el español

So both parts are natural, even though they look inconsistent from an English-speaking point of view.

Because gustar normally uses an indirect object pronoun, and the full phrase can be added for emphasis or clarity.

• me = to me
• a mí = to me as a stressed or explicit phrase

So:

• Me gusta la geografía = normal
• A mí me gusta la geografía = As for me, I like geography / I personally like geography

The pronoun me is still required even when a mí appears. The full phrase does not replace the pronoun; it reinforces it.

It is the preposition used before the person affected by gustar-type verbs.

With gustar, the structure is not like English I like X. It is more like:

• X is pleasing to me

So a mí marks the person receiving that feeling:

• a mí = to me
• a ella = to her
• a nosotros = to us

That is why the sentence uses a mí me gusta.

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

In this sentence, the thing being liked is la geografía, which is singular. So the verb is singular:

• me gusta la geografía
• me gusta el café

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

• me gustan las ciencias
• me gustan los mapas

So gusta is correct because la geografía is one subject.

Here más means more, as in I like geography more.

It usually goes before the thing being compared or emphasized:

• me gusta más la geografía

This means the speaker likes geography more than something else understood from context, here probably more than physics.

It sounds natural in Spanish to place más there after gusta.

They work differently grammatically.

Preferir

• works more like English to prefer
• the subject is the person: mi hermana prefiere...
• literally: my sister prefers...

Gustar

• works differently from English
• the subject is the thing that is pleasing
• the person is expressed with an indirect object: a mí me gusta...
• literally closer to: geography is pleasing to me

So the sentence combines two different verb patterns:

• Mi hermana prefiere física
• a mí me gusta más la geografía

They have accents for different reasons.

• física and geografía: the written accent shows the correct stressed syllable.
• mí with an accent means me after a preposition, as in a mí.
• más with an accent means more.

But mi without an accent means my:

• mi hermana = my sister

So:

• mi = my
• mí = me

That accent changes the meaning.

Yes. That would be perfectly natural.

• Me gusta más la geografía = normal neutral statement
• A mí me gusta más la geografía = adds emphasis, contrast, or clarity

In this sentence, a mí is especially useful because there is a contrast with the sister:

• Mi hermana prefiere física, pero a mí...

It helps highlight: but as for me...

Because the sentence is contrasting two preferences.

• Mi hermana prefiere física = one preference
• a mí me gusta más la geografía = a different preference

So pero = but is the natural connector. It shows opposition or contrast between the sister’s taste and the speaker’s taste.

As nouns, yes, these school subjects are feminine:

• la física
• la geografía

That is why, when an article is used, it is la.

Many school subjects ending in -a are feminine, but not all subjects behave exactly the same way in every context, so it is best to learn them with their article when possible.

A rough pronunciation guide for Spain would be:

• Mi hermana → mee ehr-MAH-nah
• prefiere → preh-FYEH-reh
• física → FEE-see-kah
• pero → PEH-roh
• a mí → ah MEE
• me gusta más → meh GOOS-tah MAHS
• la geografía → lah heh-oh-grah-FEE-ah

A few useful pronunciation notes for Spain:

• g before e or i sounds like a strong English h: geografía
• física has stress on fí
• geografía has stress on fí
• más is stressed because of the accent mark

Normally, física by itself means physics.

If you mean physical education, Spanish usually says:

• educación física

So in this sentence, física would normally be understood as the academic subject physics, especially because it is paired with geografía.