У коробці дев’яносто книг.

Because after у/в meaning in, Ukrainian uses the locative case when talking about location.

The dictionary form is коробка (box), but in the locative singular it becomes коробці:

• коробка — nominative
• у коробці — locative, in the box

So у коробці is the correct form for in the box.

This is a normal case change for many feminine nouns ending in -ка.

When коробка goes into the locative singular:

• the ending -а changes
• the consonant к changes to ц
• the new ending is -і

So:

• коробка → коробці

That consonant change may look strange at first, but it is very common in Ukrainian declension.

Both у and в can mean in.

In many cases, the choice is made for ease of pronunciation and natural flow. Ukrainian often alternates у and в to avoid awkward sound combinations.

So both of these are possible:

• У коробці дев’яносто книг.
• В коробці дев’яносто книг.

In this sentence, у коробці sounds very natural.

In Ukrainian, the present-tense verb to be is often omitted.

So a sentence like:

• У коробці дев’яносто книг.

literally looks like:

• In the box ninety books.

But it naturally means:

• There are ninety books in the box.

You can sometimes add є:

• У коробці є дев’яносто книг.

That is also correct, but the version without є is very normal and common.

Because numerals like 5, 6, 7 ... 90 usually require the noun in the genitive plural.

So after дев’яносто (ninety), the noun книга becomes книг:

• книга — book
• книг — of books / books after numbers like 5+

That is why Ukrainian says:

• дев’яносто книг

not:

• дев’яносто книги

Книг is the genitive plural of книга.

Forms:

• книга — nominative singular
• книги — nominative plural
• книг — genitive plural

In this sentence, книг is used because of the numeral дев’яносто.

The apostrophe shows that the consonant before я is not softened. It separates the sounds a bit.

So дев’яносто is pronounced roughly like:

• dev-ya-NO-sto

The important part is в’я = vya, not a softened в.

For an English speaker, it may help to hear it as:

• dev + YA + no + sto

with the middle part clearly sounding like ya.

Yes. Ukrainian word order is more flexible than English word order.

The neutral version here is:

• У коробці дев’яносто книг.

But you could also say:

• Дев’яносто книг у коробці.

That can shift the emphasis slightly, for example toward ninety books rather than in the box.

So the original sentence is natural, but it is not the only possible order.

Yes, in a practical sense the whole phrase дев’яносто книг functions as the thing that exists in the box.

So the structure is basically:

• У коробці — location
• дев’яносто книг — what is there

Even though книг is in the genitive plural, the full numeral phrase acts like the main noun phrase of the sentence.

It means exactly ninety.

If a speaker just wanted to say a lot of books, they would normally use a different expression, such as:

• багато книг — many books

So дев’яносто книг is a precise quantity, not just a general impression.