Moja sestra radije umuti jaja mikserom nego ručno.

Because moja has to agree with sestra in gender, number, and case.

• sestra is feminine singular nominative
• so the possessive adjective must also be feminine singular nominative
• that gives moja

Compare:

• moj brat = my brother
• moja sestra = my sister
• moje dijete = my child

Radije is an adverb meaning rather / preferably.

It is used to express preference:

• radije pijem čaj nego kavu = I’d rather drink tea than coffee
• radije idem pješice = I prefer to go on foot

In this sentence, radije modifies the verb and shows what your sister prefers to do.

It comes from rado (gladly, willingly) and radije is its comparative form, so it literally works like more willingly.

Because Croatian commonly uses the pattern:

radije ... nego ... = rather ... than ...

So:

• radije mikserom nego ručno
• radije ostaje doma nego izlazi
• radije čitam nego gledam televiziju

Here nego introduces the thing being contrasted with the preferred option.

This is about aspect, which is very important in Croatian verbs.

• mutiti = imperfective, focusing on the process of beating/mixing
• umutiti = perfective, focusing on getting the result, beating something up properly/completely

So:

• muti jaja suggests the activity itself
• umuti jaja suggests successfully beating the eggs

A learner should know that in a general or habitual statement, many speakers might also say radije muti jaja.... Using umuti adds a more result-oriented feel.

Also, umuti here is 3rd person singular present of umutiti.

Yes, by itself umuti can also be the imperative form meaning beat! / whisk!

But in this sentence it is clearly not an imperative, because the subject moja sestra is stated:

• Moja sestra umuti jaja = My sister beats / will beat the eggs
• Umuti jaja! = Beat the eggs!

So context removes the ambiguity.

Here jaja is accusative plural, because it is the direct object of the verb.

The tricky part is that for many neuter plural nouns, nominative plural and accusative plural look the same.

• singular: jaje = egg
• plural: jaja = eggs

So in this sentence:

• umuti što? → jaja

That makes jaja the object.

Because Croatian uses the instrumental case to show the instrument or means used to do something.

So:

• mikser = mixer
• mikserom = with a mixer

This is very common with tools and means of doing something:

• pišem olovkom = I write with a pencil
• režem nožem = I cut with a knife
• idem autobusom = I go by bus

No preposition is needed here. The case ending itself shows the meaning with/by means of.

Because ručno is an adverb meaning by hand / manually, and it is a very natural opposite to doing something with a machine.

So the contrast is:

• mikserom = with a mixer
• ručno = manually / by hand

Rukom literally means with the hand, using the instrumental of ruka. That is grammatical, but it sounds more literal and physical.

Compare:

• napisao je pismo rukom = he wrote the letter by hand
• radije to radi ručno = he prefers to do it manually

In this sentence, ručno is the more idiomatic choice because it contrasts neatly with using a mixer.

Because Croatian does not have articles.

So nouns appear without words corresponding directly to English a/an and the. Whether something is definite or indefinite is understood from context.

That is why Croatian simply says:

• moja sestra
• jaja
• mikserom

without any article.

No. Croatian word order is fairly flexible, although some orders sound more neutral than others.

The given sentence is natural and clear:

Moja sestra radije umuti jaja mikserom nego ručno.

But you could also hear variations such as:

• Moja sestra radije jaja umuti mikserom nego ručno.
• Moja sestra jaja radije umuti mikserom nego ručno.
• Mikserom moja sestra radije umuti jaja nego ručno.

These alternatives shift emphasis more than meaning. The original order is a good neutral one for learners.

Yes, often you can.

For example:

• Moja sestra više voli umutiti jaja mikserom nego ručno.

That means something like My sister prefers to beat eggs with a mixer rather than by hand.

The difference is mainly style and structure:

• radije is a compact adverb meaning rather
• više voli literally means likes more / prefers

Both are common, but radije ... nego ... is a very useful pattern to learn.

It can depend on context, but the aspect matters.

Because umuti is perfective, it tends to point to a completed action/result. That can make the sentence feel a bit more like a specific choice in a situation.

If you want a strongly habitual or general statement, many learners will more often see the imperfective:

• Moja sestra radije muti jaja mikserom nego ručno.

That sounds more clearly like a regular preference or habit.

So the version with umuti is understandable, but it has a more result-focused flavor than muti.

Because radije normally expresses preference about the action as a whole, not just about one noun.

In this sentence, the full idea is:

• she would rather beat the eggs with a mixer than do it by hand

So radije scopes over the action, while mikserom and ručno are the two contrasted ways of doing it.

A useful pattern to remember is:

Subject + radije + verb + X nego Y

where X and Y are the two options being compared.