Cartea de îmbarcare este în bagajul de mână.

Because Romanian usually puts the definite article at the end of the noun.

• carte = book
• cartea = the book

Here, cartea de îmbarcare means the boarding pass.
The noun carte is feminine, so its definite singular form is cartea.

de îmbarcare means something like for boarding or boarding-related.

So:

• carte = book
• cartea de îmbarcare = boarding pass

This is just the normal Romanian way to build this expression. Even though carte usually means book, in some set expressions it can refer to a pass, booklet, or card-like document.

In both cases, de links the main noun to another word that describes its type or purpose.

• cartea de îmbarcare = the boarding pass
• bagajul de mână = the hand luggage / carry-on bag

So de often works like of, for, or sometimes just forms a fixed expression in English translation.

It does not always translate word-for-word the same way, but it is very common in Romanian noun phrases.

For the same reason as cartea: Romanian adds the definite article to the end of the noun.

• bagaj = luggage / baggage
• bagajul = the luggage / the bag

So în bagajul de mână means in the carry-on bag or in the hand luggage.

Literally, de mână means of hand or by hand.

In travel language, bagaj de mână is the normal expression for:

• hand luggage
• carry-on baggage

So bagajul de mână is a fixed phrase you should learn as a chunk.

Romanian uses the singular in this fixed expression: bagaj de mână.

English also often uses the singular in similar expressions:

• hand luggage
• hand bag
• carry-on bag

So this is just the standard Romanian form, not something you need to translate literally.

In this sentence, este is normally used.

• Cartea de îmbarcare este în bagajul de mână.

That is the standard full form meaning The boarding pass is in the carry-on bag.

In casual speech, Romanians often use e instead of este:

• Cartea de îmbarcare e în bagajul de mână.

That sounds natural and very common. But completely dropping the verb here would not be standard.

Yes, Romanian word order is somewhat flexible, but the given version is the most neutral and natural:

• Cartea de îmbarcare este în bagajul de mână.

You might also hear something like:

• În bagajul de mână este cartea de îmbarcare.

That puts more emphasis on where it is.
Still, for a learner, the original sentence is the best basic model.

A simple approximate pronunciation is:

KAR-tya de im-bar-KA-re YES-te in ba-GA-jul de MUN-uh

A few helpful notes:

• c before a sounds like k
• ă is a short central vowel, similar to the unstressed vowel in sofa
• â and î are the same sound in modern Romanian pronunciation
• j in bagajul sounds like the s in measure

So:

• cartea ≈ KAR-tya
• îmbarcare ≈ im-bar-KA-re
• bagajul ≈ ba-GA-jul
• mână ≈ MUN-uh

They both mean is.

• este = full form, a bit more formal or careful
• e = shorter everyday form

So these are both correct:

• Cartea de îmbarcare este în bagajul de mână.
• Cartea de îmbarcare e în bagajul de mână.

As a beginner, it is good to recognize both.

It is the standard and safest expression to learn.

Depending on context, you might also hear words like bilet in travel situations, but boarding pass specifically is best learned as:

• carte de îmbarcare = a boarding pass
• cartea de îmbarcare = the boarding pass

So if you want to say exactly boarding pass, this is the right phrase.