Діти люблять стрибати через калюжі, але я прошу їх не бігти дорогою.

Люблять is the 3rd person plural form of любити (to love / to like).

• Діти = children
• Since the subject is plural, the verb must also be plural:
  • дитина любить = the child likes
  • діти люблять = the children like

So Діти люблять... means The children like...

After verbs like любити (to like / to love), Ukrainian commonly uses an infinitive, just like English does:

• люблять стрибати = like to jump
• люблю читати = I like to read
• він любить співати = he likes to sing

So Діти люблять стрибати is a very natural structure meaning The children like to jump.

Стрибати is the imperfective verb, which often suggests a repeated, general, or habitual action.

Here the meaning is something like:

• Children like jumping over puddles
• Children like to jump over puddles

That is a general habit, not one single jump.

Compare:

• стрибати = to jump / to be jumping / to jump repeatedly
• стрибнути = to make one jump / to jump once

So люблять стрибати fits much better than люблять стрибнути, because the sentence talks about a general tendency.

Here через means over or across.

So:

• стрибати через калюжі = to jump over puddles

This preposition is often used when crossing from one side to another, or moving over something:

• через міст = across the bridge
• через дорогу = across the road
• через калюжі = over / across puddles

The preposition через normally takes the accusative case.

The noun is:

• калюжа = puddle

Its plural nominative is:

• калюжі = puddles

Its plural accusative for an inanimate noun is also:

• калюжі

So although you see калюжі, that form is functioning as accusative plural here.

In other words:

• dictionary form: калюжа
• after через: через калюжі

Прошу їх means I ask them.

Breakdown:

• прошу = I ask / I request
• їх = them

So:

• я прошу їх = I ask them

This is a very common pattern in Ukrainian:

• Я прошу тебе почекати. = I ask you to wait.
• Ми просимо вас сісти. = We ask you to sit down.

Їх is one of the forms of the pronoun вони (they).

Here it is the object of прошу, so it means them:

• вони = they
• їх = them / their (depending on context)

In this sentence:

• я прошу їх = I ask them

So їх is not possessive here; it is the direct object of the verb.

After просити (to ask), Ukrainian often uses an infinitive to express what someone is being asked to do or not do.

So:

• прошу їх не бігти = I ask them not to run

This is very similar to English:

• I ask them not to run
• Я прошу їх не бігти

The не simply negates the infinitive:

• бігти = to run
• не бігти = not to run

Бігти is the normal infinitive meaning to run.

In this sentence it works well because the speaker is asking them not to perform that action.

Also, Ukrainian often uses verb aspect and motion verbs carefully, but here бігти is the straightforward choice for to run.

The phrase:

• не бігти дорогою

means something like:

• not to run on the road
• not to run along the road

depending on context.

Дорогою is the instrumental singular form of дорога (road).

• дорога = road
• дорогою = by/along/on the road

In Ukrainian, the instrumental case is often used in an adverbial way to show the route or path along which movement happens.

So:

• бігти дорогою = to run along the road / on the road

This use may feel unusual to English speakers, because English uses a preposition, while Ukrainian can often express it just with the instrumental case.

Yes. Ukrainian word order is fairly flexible, though the original sentence is the most neutral and natural:

• Діти люблять стрибати через калюжі, але я прошу їх не бігти дорогою.

You could move things around for emphasis, for example:

• Я прошу їх не бігти дорогою, але діти люблять стрибати через калюжі.

That changes the focus slightly, but the grammar still works.

So word order in Ukrainian is often about emphasis, not just grammar. The original version sounds neutral and straightforward.

Because але means but, and in Ukrainian it normally introduces a new clause, just as in English:

• Діти люблять стрибати через калюжі, але я прошу їх не бігти дорогою.

There are two parts here:

1. Діти люблять стрибати через калюжі
2. я прошу їх не бігти дорогою

They are joined by але = but, so a comma is used before it.

Ukrainian does not have articles.

So where English says:

• the children
• the puddles
• the road

Ukrainian simply says:

• діти
• калюжі
• дорога / дорогою

Whether something is the, a, or just general is understood from context.

In this sentence:

• Діти can mean children or the children
• калюжі can mean puddles or the puddles
• дорогою can mean on the road / along the road

The exact interpretation comes from the situation, not from an article.