eki no kenbaiki de kippu wo kau mae ni, untin wo kakuninsimasita.

Yes, の links nouns together.

• 駅 = station
• 券売機 = ticket machine / ticket vending machine

So 駅の券売機 literally means the station's ticket machine, but in natural English it usually means the ticket machine at the station.

In Japanese, AのB often means:

• B belonging to A
• B located at A
• B associated with A

So here it is not necessarily possession in the strict English sense.

券売機 is a compound noun:

• 券 = ticket
• 売 = sell
• 機 = machine

So it literally means ticket-selling machine, usually translated as ticket machine or ticket vending machine.

This is a very common type of Japanese compound noun, where several kanji combine into one word.

で marks the place where an action happens.

In 駅の券売機で切符を買う, the action buying a ticket happens at/using the ticket machine.

So で can suggest:

• the location of the action: at the ticket machine
• the means/tool used: using the ticket machine

Both ideas fit here, and in English we often just say from the ticket machine or at the ticket machine.

Before 前に, Japanese normally uses the dictionary form of the verb when the action has not happened yet relative to that point.

So:

• 買う前に = before buying
• literally, before (I) buy

This is the standard pattern:

• V dictionary form + 前に = before doing V
• Noun + の + 前に = before noun

Examples:

• 寝る前に = before sleeping
• 食事の前に = before the meal

So 切符を買う前に is the correct form.

前に means before.

The part before it is the action that has not happened yet at that moment:

• 切符を買う前に = before buying a ticket

Then the main clause tells you what happened before that:

• 運賃を確認しました = checked the fare

So the whole sentence means:

• Before buying a ticket at the station ticket machine, I checked the fare.

This is a very common way to connect actions in Japanese.

Because the main action of the sentence is 確認しました.

Japanese tense usually appears at the end of the clause and tells you when that clause happened.

• 買う前に is a before expression, so 買う stays in dictionary form
• 確認しました is the main event being reported, so it is in the past polite form

So the timeline is:

1. check the fare
2. buy the ticket

But grammar-wise:

• 買う前に = before buying
• 確認しました = checked

They are related, but not the same.

• 切符 = ticket
• 運賃 = fare

So:

• 切符を買う = buy a ticket
• 運賃を確認する = check the fare

A fare is the amount of money you need to pay. A ticket is the thing you buy.

Because both are direct objects of verbs.

• 切符を買う = buy a ticket
• 運賃を確認しました = checked the fare

The particle を marks what the verb acts on.

So in this sentence:

• the thing being bought is 切符
• the thing being checked is 運賃

確認する means more than just casually looking. It often means:

• confirm
• verify
• make sure of

So 運賃を確認しました can mean:

• I checked the fare
• I confirmed the fare
• I made sure what the fare was

It sounds a bit more careful or deliberate than a very casual looked at.

Sometimes, but 切符 is the more natural word here.

• 切符 is commonly used for train tickets and similar transportation tickets
• チケット is used more for event tickets, movie tickets, concert tickets, and sometimes other kinds of tickets

At a train station, 切符 is the standard choice.

The comma helps separate the introductory part from the main clause:

• 駅の券売機で切符を買う前に、
• 運賃を確認しました。

It makes the sentence easier to read, especially because the before... phrase is fairly long.

Japanese commas are often optional in places like this, so you may also see:

• 駅の券売機で切符を買う前に運賃を確認しました。

Both are fine.

A simple breakdown is:

• 駅の券売機で = at/using the station ticket machine
• 切符を買う前に = before buying a ticket
• 運賃を確認しました = checked the fare

So the overall structure is:

[Place/method] + [action before which something happens] + [main action]

Japanese often puts background information first and the main action at the end.

Yes, the subject is omitted.

Japanese often leaves out the subject when it is clear from context. So this sentence does not explicitly say:

• I checked the fare
• he/she checked the fare
• they checked the fare

In many textbook contexts, it is understood as I.

This is completely normal in Japanese. You do not need to state the subject unless it is important.

Usually 駅の券売機で is more natural here.

• 駅の券売機 clearly means the ticket machine at the station
• 駅で券売機で sounds repetitive because you would have two で phrases in a row, and the relationship between station and ticket machine is less neatly expressed

Japanese often prefers noun linking with の when one noun naturally modifies another, as in:

• 学校の図書館 = the school library
• 駅のホーム = the station platform
• 駅の券売機 = the station ticket machine

In this context, 運賃 usually means the transportation fare, especially for trains or buses.

It is the amount you need to pay to travel from one station to another.

This is different from some other money-related words:

• 料金 = fee/charge in a broader sense
• 運賃 = transportation fare specifically

Because the sentence is about buying a ticket at a station, 運賃 is exactly the right word.