Гарантійний талон лежить у коробці.

Because гарантійний is an adjective, and it has to agree with талон in gender, number, and case.

Here, талон is:

• masculine
• singular
• nominative

So the adjective also takes the masculine singular nominative form:

• гарантійний талон

If the noun changed, the adjective would change too. For example:

• гарантійна коробка = a warranty box / guaranteed box-like phrase structure
• гарантійне обслуговування = warranty service
• гарантійні талони = warranty cards

Талон is in the nominative singular.

It is the subject of the sentence — the thing that is doing the action of лежить.

So the structure is:

• Гарантійний талон = subject
• лежить = verb
• у коробці = location

Yes, лежить literally means lies / is lying.

In Ukrainian, verbs like лежати are often used to describe where something is located, especially when it is physically resting somewhere. So:

• Гарантійний талон лежить у коробці
  can mean both:
• The warranty card is lying in the box
• more naturally in English, The warranty card is in the box

Ukrainian often uses a more concrete verb here than English does.

Лежить is:

• present tense
• 3rd person singular
• from the verb лежати = to lie

So it matches the singular subject талон.

A few related forms:

• я лежу = I am lying
• ти лежиш = you are lying
• він / вона / воно лежить = he / she / it is lying
• вони лежать = they are lying

Because after у meaning in, when you are talking about location, Ukrainian uses the prepositional case.

The dictionary form is:

• коробка = box

But after у for location, it becomes:

• у коробці = in the box

So:

• коробка = nominative
• у коробці = prepositional

This is a very common pattern with place expressions.

Коробці is in the prepositional singular.

The preposition у here means in, and with location it requires the prepositional case.

So:

• у коробці = in the box
• у кімнаті = in the room
• у магазині = in the store

For a native English speaker, this is one of the most important things to notice: Ukrainian changes the noun form after many prepositions.

Yes, в коробці is also possible.

Both у and в can mean in. Very often the choice is made for ease of pronunciation and smoother sound.

Ukrainian alternates between them to avoid awkward consonant clusters or awkward vowel sequences.

So both of these are fine:

• Гарантійний талон лежить у коробці
• Гарантійний талон лежить в коробці

In many contexts, one will simply sound smoother than the other.

Because Ukrainian usually does not use the present-tense verb to be the way English does.

In English, you say:

• The card is in the box

In Ukrainian, present-tense бути is normally omitted in simple statements like this.

Also, this sentence uses лежить instead of just an implied is, because it describes the item as physically lying there.

So Ukrainian does not need a separate word meaning is here.

Yes. Ukrainian word order is quite flexible.

The neutral order here is:

• Гарантійний талон лежить у коробці.

But you could also say:

• У коробці лежить гарантійний талон.

That version puts more focus on where it is.

Very roughly:

• Гарантійний талон лежить у коробці = neutral, starting with the item
• У коробці лежить гарантійний талон = more like In the box is the warranty card

The meaning stays basically the same, but the emphasis changes.

Because in Ukrainian, as in English, noun phrases are often built with an adjective + noun structure.

Here:

• гарантійний = warranty-related / guarantee-related
• талон = slip, card, coupon, stub, form, depending on context

Together, гарантійний талон is a standard expression for a warranty card or warranty slip.

So even if талон can mean several kinds of paper slips in different contexts, the whole phrase gives the intended meaning.

Yes, that is a very good rule of thumb.

In Ukrainian, nouns that end in a hard consonant are very often masculine.

So:

• талон → masculine

That is why:

• the adjective is гарантійний
• the verb is singular and agrees with a singular subject

Of course, there are exceptions elsewhere in the language, but for nouns like талон, this rule works well.

The ending changes because of case, and the sound change is normal.

Dictionary form:

• коробка

After у for location:

• у коробці

What happened?

• the noun is feminine
• it goes into the prepositional singular
• many feminine nouns in -ка change to -ці in this form

So this is not random — it is part of a common declension pattern.

A rough pronunciation guide:

• коробка ≈ ko-ROB-ka
• коробці ≈ ko-rob-TSI

You usually would not say that in this kind of simple sentence.

While є can appear in Ukrainian, it is not normally used as a direct equivalent of English is in basic location statements.

So:

• natural: Гарантійний талон лежить у коробці.
• also possible depending on style: Гарантійний талон у коробці.
• less natural here: Гарантійний талон є у коробці.

For learners, the safest choice is to avoid inserting є just because English has is.