היא מזמינה אותנו הביתה, כי היא רוצה להראות לנו את הספרים החדשים שלה.

A natural pronunciation is:

Hi mazmina otanu habayta, ki hi rotza lehar'ot lanu et hasfarim hachadashim shela.

A few helpful notes:

• היא = hi
• מזמינה = mazmina
• הביתה = habayta
• רוצה here is pronounced rotza because the subject is feminine
• להראות = lehar'ot

Because the subject is היא = she.

In the present tense, Hebrew verbs agree with gender and number:

• מזמין = masculine singular
• מזמינה = feminine singular

So with היא, you need מזמינה.

אותנו means us.

It is the direct object pronoun used after a verb like invite:

• היא מזמינה אותנו = she invites us

Hebrew often uses special object forms like:

• אותי = me
• אותך = you
• אותו = him
• אותה = her
• אותנו = us

So אותנו is not just a random word for us; it is specifically the direct object form.

In הביתה, the final -ה is a directional ending. It gives the sense of to home or homeward.

So:

• הביתה = home / to the house / toward home

This is different from:

• הבית = the house
• בבית = at home / in the house

In this sentence, מזמינה אותנו הביתה means she is inviting us over to her home.

כי means because here.

It introduces the reason:

• כי היא רוצה... = because she wants...

So the sentence has two parts:

• she invites us home
• because she wants to show us something

In other contexts, כי can sometimes mean that, but here it clearly means because.

In unpointed Hebrew, רוצה can represent both:

• rotze = masculine singular
• rotza = feminine singular

The spelling is the same, but the pronunciation and meaning depend on context.

Here the subject is היא, so it must be feminine:

• היא רוצה = she wants

If it were he wants, it would also be written הוא רוצה, but pronounced rotze.

Because להראות means to show, while לראות means to see.

They are related in meaning, but they are different verbs:

• לראות = to see
• להראות = to show

So:

• היא רוצה להראות לנו... = she wants to show us...

This is a very common pair for learners to confuse.

לנו means to us.

With להראות = to show, Hebrew usually uses:

• the thing being shown as the direct object
• the person receiving it with ל־

So:

• להראות לנו את הספרים = to show us the books

Literally, it is closer to to show to us the books, even though in natural English we usually say show us the books.

את marks a definite direct object.

It does not get translated into English, but it is an important grammar marker in Hebrew.

Here:

• את הספרים החדשים שלה = the direct object, her new books

Because the books are definite, Hebrew uses את before them.

Because in Hebrew, adjectives follow the noun and match it in:

• gender
• number
• definiteness

So:

• ספרים = books
• חדשים = new, masculine plural
• הספרים החדשים = the new books

Since the noun is definite, the adjective must also be definite.

That is why you get:

• הספרים החדשים not
• הספרים חדשים

Because ספרים is masculine plural.

Hebrew adjectives must agree with the noun they describe:

• חדש = masculine singular
• חדשה = feminine singular
• חדשים = masculine plural
• חדשות = feminine plural

Since ספרים is masculine plural, the adjective must be חדשים.

Hebrew often puts the possessive pronoun after the noun phrase.

So:

• הספרים החדשים שלה = her new books

Literally, the order is more like:

• the books the new her

This is normal Hebrew word order.

Notice that the adjective still comes right after the noun:

• ספרים חדשים and then the possessive comes after that:
• ספרים חדשים שלה

It is repeated because the second clause has its own subject:

• היא מזמינה אותנו הביתה
• כי היא רוצה להראות לנו...

In Hebrew, this is very natural. In fact, in the present tense, subject pronouns are often helpful because the verb form does not always clearly show the person by itself.

So repeating היא makes the sentence clear and normal.