У році дванадцять місяців.

Because у means in, and after this preposition Ukrainian uses the locative case here.

So:

• рік = year (dictionary form, nominative)
• у році = in the year / in a year (locative)

The form році is the locative singular of рік.

Because Ukrainian numbers affect the form of the noun that follows them.

With 5 and higher, the noun usually goes into the genitive plural:

• п’ять місяців = five months
• десять місяців = ten months
• дванадцять місяців = twelve months

So місяців is the correct form after дванадцять.

A very useful pattern is:

• 1 → nominative singular
• 2, 3, 4 → a special plural pattern
• 5+ → genitive plural

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

So:

• У році дванадцять місяців. literally: In a year twelve months. natural meaning: There are twelve months in a year.

You may sometimes see є used for emphasis or clarity, but very often it is simply left out.

So this sentence could also be understood as:

• У році є дванадцять місяців.

But the version without є is completely normal.

Yes, often you can. у and в are very often variants of the same preposition, and speakers choose between them for ease of pronunciation and smooth sound.

So both can be possible:

• У році дванадцять місяців.
• В році дванадцять місяців.

However, у році sounds very natural here.

This у / в alternation is extremely common in Ukrainian.

No, Ukrainian word order is fairly flexible.

This sentence:

• У році дванадцять місяців.

can also be said as:

• Дванадцять місяців у році.

Both are understandable. The difference is mostly about focus and style, not basic meaning.

Roughly:

• У році дванадцять місяців = starts with the setting, in a year
• Дванадцять місяців у році = starts with the quantity, twelve months

This is just a normal language difference.

Ukrainian often uses the singular noun in this kind of general statement:

• У році дванадцять місяців. literally: In the year there are twelve months

But the meaning is general, just like English in a year.

So you should not translate too word-for-word. The sentence means the general fact, not one specific year.

It is the genitive plural of місяць.

The forms are:

• місяць = month
• місяці = months
• місяців = of months / used after numbers like 5+

In this sentence, дванадцять requires that genitive plural form, so we get:

• дванадцять місяців

A simple learner-friendly pronunciation is roughly:

• у році ≈ u ROT-si

A few helpful points:

• р is a rolled or tapped r
• ц sounds like ts
• і sounds like ee in see

So році is approximately ROT-see, though the real Ukrainian sound is a bit softer and more precise than English spelling suggests.

Because they are different case forms.

From рік:

• року = genitive singular
• році = locative singular

In this sentence, the preposition у means in, so Ukrainian uses the locative:

• у році

You might see року in phrases like:

• цього року = this year
• минулого року = last year

So both forms are correct, but they are used in different grammar patterns.

Yes, that is grammatical.

• Є дванадцять місяців у році. = There are twelve months in a year.

It sounds a little more explicit because it includes є = there is/are.

But in everyday Ukrainian, the shorter version without є is very common:

• У році дванадцять місяців.

So both work, but the original sentence is natural and standard.