В кабине для звонков работает скоростной интернет.

Because в кабине answers the question where? and shows a static location: in the booth.

• в + prepositional = location
  
  • в кабине = in the booth
• в + accusative = motion into something
  
  • в кабину = into the booth

So this sentence is talking about where the internet is available, not movement into the booth.

Here кабина means something like a booth, cubicle, or small enclosed cabin/space.

In this context, кабина для звонков is a phone booth or a call booth. It does not mean a vehicle cabin or cockpit here, even though кабина can mean those in other contexts.

Because для means for, and it requires the genitive case.

• dictionary form: звонок = call, phone call
• after для, it becomes звонков

So:

• кабина для звонков = a booth for calls

This is a very common Russian pattern:

• комната для встреч = a room for meetings
• чашка для чая = a cup for tea

The plural gives a general meaning: for making calls, for calls in general.

• для звонков = for calls, for phone calls generally
• для звонка = for a call, for one specific call

In English, we often use a singular noun in this kind of phrase, but Russian often prefers the plural when talking about a general purpose.

In Russian, работать is often used not only for people but also for machines, systems, services, and connections. So интернет работает means:

• the internet is working
• the internet functions
• the internet is available and operating properly

This is very natural Russian. You can also say things like:

• Wi‑Fi не работает = the Wi‑Fi isn’t working
• Сайт работает = the website is working

So here работает does not mean the internet is literally doing a job; it means it functions.

You could say В кабине для звонков есть скоростной интернет, but the nuance is a little different.

• есть focuses on existence/presence: there is high-speed internet
• работает focuses on functioning/availability: the high-speed internet works / is up and running

So работает sounds a bit more practical: the connection is not just present, it actually functions.

Скоростной means high-speed or fast-speed. It comes from скорость, meaning speed.

So скоростной интернет = high-speed internet.

A few nuance notes:

• скоростной интернет is understandable and natural enough
• высокоскоростной интернет is a bit more formal or technical
• быстрый интернет is more everyday and conversational

All three can refer to fast internet, but скоростной sounds slightly more descriptive and label-like.

Because it agrees with интернет.

Here интернет is:

• masculine
• singular
• nominative (because it is the subject)

So the adjective must also be:

• masculine
• singular
• nominative

That gives скоростной интернет.

You can also see the agreement in the verb:

• интернет работает
  singular subject → singular verb

The subject is скоростной интернет.

You can tell because:

• it is in the nominative case
• the verb работает agrees with it in singular
• it is the thing that is functioning

So the structure is basically:

• В кабине для звонков = location
• работает = verb
• скоростной интернет = subject

Russian word order is flexible, so the subject does not have to come first.

Russian often puts the location, time, or other context at the beginning to set the scene.

So:

• В кабине для звонков работает скоростной интернет

feels like:

• As for the call booth, high-speed internet works there
• In the call booth, high-speed internet is available

This word order is natural if the place is important information. A different order is also possible, for example:

• Скоростной интернет работает в кабине для звонков

But the original sentence sounds more like it is introducing or highlighting the location first.

Because Russian has no articles.

So кабина can mean:

• a booth
• the booth

and интернет can mean:

• internet
• the internet

You understand which one is meant from context. That is normal in Russian, and learners usually have to get used to relying more on context than on articles.