Der Waggon ist voll, aber das Abteil hinten ist fast leer.

German nouns have grammatical gender, and you have to learn each noun with its article:

• der Waggon = masculine
• das Abteil = neuter

In this sentence, both nouns are the subjects of their clauses, so they appear in the nominative case:

• Der Waggon ist voll
• das Abteil hinten ist fast leer

There is no special rule that tells you from the meaning why one is masculine and the other is neuter; it is mostly something you memorize with the noun.

Because voll and leer are being used as predicate adjectives, not directly before a noun.

After sein and similar verbs, German adjectives usually do not take endings:

• Der Waggon ist voll.
• Das Abteil ist leer.

Compare that with adjectives placed before a noun, where endings are required:

• ein voller Waggon
• ein leeres Abteil

So here, voll and leer stay in their basic form.

The conjunction aber means but. It connects two main clauses. After aber, German still keeps normal main-clause word order, which means the conjugated verb is in second position.

So the pattern is:

• Der Waggon | ist | voll
• aber das Abteil hinten | ist | fast leer

That is why ist comes after the subject phrase das Abteil hinten.

This is different from conjunctions like weil, which send the verb to the end.

Hinten means at the back or in the back.

Here it describes which compartment is meant:

• das Abteil hinten = the compartment in the back

It is working like an adverbial expression attached to the noun phrase. In natural English, we often translate it with a relative phrase such as the compartment at the back.

German often allows this kind of compact structure:

• der Mann dort = the man there
• das Haus links = the house on the left
• das Abteil hinten = the compartment at the back

Yes. Those are related but slightly different ways to express the idea.

• das Abteil hinten = the compartment at the back
• das hintere Abteil = the rear compartment / the back compartment
• im hinteren Abteil = in the rear compartment

In your sentence, das Abteil hinten is a very natural way to point out location.
Das hintere Abteil sounds a bit more like a fixed descriptive label.

So:

• Das Abteil hinten ist fast leer.
• Das hintere Abteil ist fast leer.

Both are possible.

Fast means almost.

So:

• fast leer = almost empty

It is placed before the adjective it modifies:

• fast leer
• fast voll
• fast fertig

That is similar to English almost empty, almost full, almost finished.

Yes, Waggon is a real and understandable word, meaning a railway car or carriage. But in modern everyday German, Wagen is often more common, depending on context.

Some related words:

• der Waggon = carriage / railcar
• der Wagen = vehicle, car, carriage, wagon
• der Zugwagen = railcar / coach, depending on context

A native speaker will understand Waggon, but it can sound a little more formal, old-fashioned, or railway-specific than Wagen.

Because in German, all nouns are capitalized.

So in this sentence:

• der Waggon
• das Abteil

are capitalized because they are nouns.

But words like voll, fast, leer, and hinten are not nouns here, so they are lowercase.

This is one of the most noticeable spelling differences between German and English.

Ist is the third-person singular form of sein = to be.

Both subjects are singular:

• der Waggon = singular
• das Abteil = singular

So both clauses use ist:

• Der Waggon ist voll.
• Das Abteil hinten ist fast leer.

If the subject were plural, you would use sind instead:

• Die Waggons sind voll.
• Die Abteile sind fast leer.

Yes. Aber is a coordinating conjunction. That means it connects two equal main clauses and does not push the verb to the end.

So you get:

• Der Waggon ist voll, aber das Abteil hinten ist fast leer.

Compare that with a subordinating conjunction like obwohl:

• Der Waggon ist voll, obwohl das Abteil hinten fast leer ist.

Notice how with obwohl, the verb ist moves to the end of the subordinate clause.

So a very useful rule is:

• aber = normal main-clause word order
• weil / obwohl / dass = verb goes to the end

Yes. Voll and leer are opposites, but the sentence creates a contrast:

• Der Waggon ist voll = the carriage as a whole is full
• das Abteil hinten ist fast leer = one compartment in the back is still mostly empty

So the idea is that the overall situation and the local situation are different. The carriage may seem crowded, but one specific section is not.

That contrast is exactly why aber is used.