У коробці шістнадцять яблук.

It is in the locative case.

After у/в when you mean in a place, Ukrainian usually uses the locative:

• коробка = box
• у коробці = in the box / in a box

So коробці is the form of коробка used after у for location.

That is a normal sound and spelling change in Ukrainian.

With some feminine nouns ending in -ка, the к changes to ц before endings with -і in forms like the locative:

• коробка → у коробці
• рука → у руці

So this is not an irregular one-off form; it is part of a common pattern.

Because after шістнадцять and most numbers from 5 upward, Ukrainian uses the noun in the genitive plural.

The dictionary form is яблуко (apple), but after 16 you get:

• шістнадцять яблук

Compare:

• одне яблуко = one apple
• два яблука = two apples
• п'ять яблук = five apples
• шістнадцять яблук = sixteen apples

So яблук is the correct counting form here.

The dictionary form is яблуко, which means apple.

In this sentence, яблук is just a changed form of яблуко used after the number шістнадцять.

Yes, from an English point of view it may feel like something is missing, but in Ukrainian this is normal.

In the present tense, Ukrainian often omits the verb to be. So:

• У коробці шістнадцять яблук.

literally feels like:

• In the box sixteen apples.

This naturally means:

• There are sixteen apples in the box.

You can also say:

• У коробці є шістнадцять яблук.

That is also correct, with є making the existence a bit more explicit.

Yes. у and в both mean in here.

The choice is usually made for smooth pronunciation:

• у коробці
• в коробці

Both are correct. Speakers often choose whichever sounds easier next to the surrounding words. In this sentence, у коробці is very natural.

Yes, you can change the word order.

Ukrainian word order is more flexible than English.
У коробці шістнадцять яблук is a very natural way to present the information, especially if the location is the starting point: In the box, there are sixteen apples.

You could also say:

• Шістнадцять яблук у коробці.

That is grammatical too, but it shifts the focus a little. The original sentence sounds more neutral and natural in many contexts.

Because Ukrainian has no articles.

There is no direct equivalent of English a/an or the.
So у коробці can mean:

• in the box
• in a box

The exact meaning depends on context. English has to choose a or the, but Ukrainian usually leaves that unstated.

Here are some useful comparisons:

• У коробці одне яблуко. = There is one apple in the box.
• У коробці два яблука. = There are two apples in the box.
• У коробці чотири яблука. = There are four apples in the box.
• У коробці п'ять яблук. = There are five apples in the box.
• У коробці шістнадцять яблук. = There are sixteen apples in the box.

This helps show the main pattern:

• 1 → яблуко
• 2–4 → яблука
• 5 and higher → яблук

Yes, absolutely.

Both are correct:

• У коробці шістнадцять яблук.
• У коробці є шістнадцять яблук.

The version without є is very common and natural.
The version with є can sound a little more explicit, like there exists / there are.

So as a learner, it is good to recognize both.