היא מעדיפה לנסוע באוטובוס ציבורי מאשר לקחת אוטו פרטי.

Because the subject is היא = she. In Hebrew present tense, the verb agrees with the subject’s gender and number.

• מעדיף = masculine singular
• מעדיפה = feminine singular

So היא מעדיפה means she prefers.

After a verb like מעדיפה (prefers), Hebrew normally uses the infinitive for the action being preferred.

So:

• היא מעדיפה לנסוע = she prefers to travel
• מאשר לקחת = rather than to take

This is very similar to English prefer to travel rather than take.

לנסוע means to travel / to go by vehicle / to ride. In this sentence, it is the natural verb for going by bus.

So לנסוע באוטובוס means to travel by bus or to go by bus.

The prefix ב־ often means in, on, or by. With transportation, Hebrew commonly uses it for by:

• לנסוע באוטובוס = to go by bus
• לנסוע ברכבת = to go by train

A useful detail: in normal unpointed Hebrew spelling, באוטובוס can look like it might mean in the bus, but here it is understood as indefinite because the adjective is also indefinite: אוטובוס ציבורי, not האוטובוס הציבורי.

Because Hebrew adjectives usually come after the noun they describe.

So:

• אוטובוס ציבורי = a public bus
• literally: bus public

Also, the adjective must agree with the noun. Since אוטובוס is masculine singular, the adjective is also masculine singular: ציבורי.

Here מאשר means than or rather than.

So:

• מעדיפה לנסוע באוטובוס ציבורי מאשר לקחת אוטו פרטי = she prefers to go by public bus rather than take a private car

It is a common comparison word in this kind of sentence.

לקחת literally means to take, but in Hebrew it is very common to use it with transportation in the sense of take/use:

• לקחת אוטו = take a car
• לקחת מונית = take a taxi
• לקחת אוטובוס = take a bus

So לקחת אוטו פרטי is a natural Hebrew way to say take a private car.

Because את is used before a definite direct object, and אוטו פרטי here is indefinite: a private car, not the private car.

So:

• לקחת אוטו פרטי = to take a private car
• לקחת את האוטו הפרטי = to take the private car

That is why את does not appear in the original sentence.

Both are correct, but they are slightly different in style.

• אוטו = very common everyday word for car
• מכונית = also common, but a bit more neutral or formal

Because אוטו is masculine, you get אוטו פרטי. Because מכונית is feminine, you would say מכונית פרטית.

Because אוטו is a masculine noun, so the adjective must also be masculine.

• אוטו פרטי = a private car
• מכונית פרטית = a private car

This is basic adjective agreement in Hebrew.

Sometimes yes, if the subject is already clear from context. Hebrew often omits subject pronouns.

However, in the present tense, מעדיפה by itself does not always uniquely mean she prefers. Depending on context, it could also mean I prefer or you prefer for a feminine singular speaker/addressee.

So היא is useful here because it makes the subject explicitly she.

You would change מעדיפה to the masculine singular form מעדיף:

הוא מעדיף לנסוע באוטובוס ציבורי מאשר לקחת אוטו פרטי.

Everything else stays the same.