gataa kara booru ga booruritaan ni modoru.

から marks the starting point or source of movement. In this sentence, the ball starts in the gutter, so ガターから means from the gutter.

A useful pattern is:

A から B に 戻る
= return from A to B

So here:

ガターから ボールリターンに 戻る
= return from the gutter to the ball return

が marks ボール as the subject of the verb 戻る.

In other words, the ball is the thing that performs the action of returning:

ボールが 戻る
= the ball returns

A learner might expect は instead, and は is also possible in some contexts, but it changes the feel a bit:

• ボールが戻る: focuses on the ball as the thing that returns
• ボールは戻る: presents the ball as the topic, something like as for the ball, it returns

In a simple descriptive sentence like this, が is very natural.

に marks the destination or endpoint of movement with verbs like 行く, 来る, and 戻る.

So:

ボールリターンに戻る
means
return to the ball return

This is the standard way to show where something returns to.

You may also learn that へ can mark direction, but with 戻る, に is very common because it emphasizes the actual destination.

戻る means to return or to go back.

It is an intransitive verb, which means the subject itself goes back. In this sentence, the ball itself returns:

ボールが戻る
= the ball returns

This is different from 戻す, which is the transitive form:

• 戻る = something returns
• 戻す = someone returns something

For example:

店員がボールを戻す
= The staff member returns the ball

But in your sentence, no one is actively returning it; the ball comes back on its own through the system, so 戻る is the right choice.

They are loanwords, and loanwords in Japanese are usually written in katakana.

• ガター comes from English gutter
• ボール comes from ball
• ボールリターン comes from ball return

Katakana is very common for sports terms, machine-related terms, and imported vocabulary.

Yes. The basic structure is:

ガターから = from the gutter
ボールが = the ball
ボールリターンに = to the ball return
戻る = returns

Japanese word order is more flexible than English, but the verb usually comes at the end. So this sentence is fine.

You could also say:

ボールが ガターから ボールリターンに 戻る。

That may feel a little easier for learners to parse, but both follow normal Japanese grammar.

Normally, Japanese is not written with spaces like this.

A native-style version would usually be written as:

ガターからボールがボールリターンに戻る。

Spaces are often added in textbooks or learning materials to make the sentence easier to read and to show where words and particles begin and end.

So the spaces here are for learning convenience, not standard everyday writing.

Yes, it could, depending on context:

ガターから ボールは ボールリターンに 戻る。

This is grammatical, but it has a different nuance.

• が presents the ball as the subject doing the action
• は presents the ball as the topic and may imply contrast or general description

So:

• ボールが戻る = the ball returns
• ボールは戻る = as for the ball, it returns

If you are just describing what happens, が is a very natural choice.

It is possible in some cases, but に is better here.

Compare:

• ボールリターンに戻る
• ボールリターンへ戻る

Both can mean return to the ball return, but に sounds more natural when you are thinking of the destination as the actual endpoint reached. With 戻る, that is usually what you want.

So に is the most standard choice in this sentence.

No. In this context, ガター refers to the gutter in bowling.

So it means the channel along the side of the lane where the ball can fall.

That is why ボールリターン also appears in the sentence: the whole sentence is talking about bowling equipment and ball movement.