Mi hermana prefiere llevar un moño cuando hace calor.

Because the subject is mi hermana, which is third-person singular (she). The verb preferir in the present tense changes to prefiere for él / ella / usted.

• yo prefiero
• tú prefieres
• él / ella prefiere

So Mi hermana prefiere... means My sister prefers...

Preferir is a stem-changing verb in the present tense. Its stem changes from e to ie in most forms:

• prefiero
• prefieres
• prefiere
• preferimos
• preferís
• prefieren

So prefiere is not irregular in a random way; it follows the normal pattern for this kind of verb.

After a verb like preferir, Spanish normally uses an infinitive to express what someone prefers to do.

So the pattern is:

preferir + infinitive

Examples:

• Prefiere llevar un moño.
• Prefiero comer en casa.
• Prefieren salir temprano.

This works much like English prefer to wear / prefer to eat / prefer to leave.

Here llevar means to wear or to have on, not to carry.

Spanish llevar is very common for:

• clothes: llevar un abrigo
• accessories: llevar gafas
• hairstyles or appearance: llevar el pelo corto, llevar un moño

So in this sentence it means that she prefers to wear her hair in a bun.

In this sentence, un moño means a hair bun.

In Spain, moño commonly refers to that hairstyle. Depending on the country or context, moño can sometimes mean other things too, such as a bow, but here the meaning is clearly the hairstyle because of llevar and the context of hot weather.

Because moño is being treated as a countable noun: a bun.

So llevar un moño is the natural way to say to wear a bun. The indefinite article un shows it is a bun, not a specific previously mentioned one.

Spanish often uses articles in places where English may sound a bit looser.

Because hace calor is the standard Spanish expression for it is hot or it’s hot weather.

Spanish uses hacer in several weather expressions:

• hace calor = it’s hot
• hace frío = it’s cold
• hace buen tiempo = the weather is nice
• hace viento = it’s windy

So even though it literally looks like it makes heat, you should learn hace calor as a fixed expression.

Because weather hacer is used impersonally, in third-person singular.

So Spanish says:

• hace calor
• hace frío
• hace sol

It stays singular even though English does not really have a visible subject there.

Because this sentence describes a habitual or general situation: whenever it is hot.

With cuando, Spanish uses:

• indicative for habitual, repeated, or known situations
• subjunctive for future or not-yet-realized situations

So here:

• cuando hace calor = whenever it’s hot / when it’s hot in general

Compare:

• Cuando hace calor, mi hermana prefiere llevar un moño.
  habitual
• Cuando haga calor, mi hermana llevará un moño.
  future situation

Yes. Spanish allows flexible word order, especially with time expressions like cuando hace calor.

These are both natural:

• Mi hermana prefiere llevar un moño cuando hace calor.
• Cuando hace calor, mi hermana prefiere llevar un moño.

The meaning stays basically the same. Putting cuando hace calor first gives a little more emphasis to the condition or time.

The ñ is important. It is pronounced like the ny sound in canyon.

So moño sounds roughly like MO-nyo.

Also:

• it has two syllables: mo-ño
• the stress is on the first syllable: MO-ño

Do not pronounce it like a plain n.

They are similar, but the focus is different:

• llevar un moño = to wear one’s hair in a bun
• hacerse un moño = to make or put one’s hair into a bun

So in this sentence, llevar focuses on the hairstyle she prefers to have. If you said Mi hermana prefiere hacerse un moño cuando hace calor, that would focus more on the action of putting her hair up.

Both are natural, but the nuance is slightly different.