Der Rückgabeautomat bucht das Buch zurück.

Those are the grammatical genders of the nouns:

• der Rückgabeautomat = masculine
• das Buch = neuter

In this sentence, der Rückgabeautomat is the subject, so it stays in the nominative case: der.

das Buch is the direct object, and because Buch is neuter, the article is das in both nominative and accusative. So here das Buch is accusative, but it looks the same as nominative.

• Der Rückgabeautomat is in the nominative case because it is the subject — the thing doing the action.
• das Buch is in the accusative case because it is the direct object — the thing affected by the action.

A good way to see it is:

• Who does the action? → der Rückgabeautomat
• What gets processed/returned? → das Buch

Because zurückbuchen is a separable verb.

The full infinitive is:

• zurückbuchen

In a normal main clause, the conjugated part goes to the usual verb position, and the prefix goes to the end:

• Der Rückgabeautomat bucht das Buch zurück.

This is very common in German:

• anrufen → Ich rufe dich an.
• aufmachen → Er macht das Fenster auf.
• zurückgeben → Sie gibt das Buch zurück.

So bucht ... zurück is just the split form of zurückbuchen.

Here it means something like to check back in, to register as returned, or to process the return in the system.

The verb buchen often has the idea of entering something into a system or recording it officially. In a library context, ein Buch zurückbuchen means that the system records the book as returned.

So this sentence is not really about physically giving the book back by hand. It is about the machine registering the return.

Because the subject is der Rückgabeautomat, which is third person singular: he/it.

The verb buchen is conjugated like this in the present tense:

• ich buche
• du buchst
• er/sie/es bucht
• wir buchen
• ihr bucht
• sie/Sie buchen

Since der Rückgabeautomat is singular, the correct form is bucht.

It is a compound noun:

• Rückgabe = return
• Automat = machine, automated device

So Rückgabeautomat literally means something like return machine.

German often builds long nouns this way by combining smaller words into one. The last part usually tells you the basic type of thing it is. Here the last part is Automat, so the whole word is a kind of machine.

That is also why the gender is der: der Automat is masculine, so der Rückgabeautomat is masculine too.

Yes, that is possible, but it has a slightly different feel.

• gibt ... zurück = gives back / returns
• bucht ... zurück = checks back in / registers as returned

In a library context, zurückbuchen is more specific because it focuses on the book being processed in the system.

So if the machine is officially recording the return, bucht ... zurück is a very natural choice.

Because in a main clause with a separable verb, the prefix is sent to the end.

German main-clause word order usually puts the conjugated verb in the second position:

• Der Rückgabeautomat bucht das Buch zurück.

Here:

• bucht = the conjugated verb part
• zurück = the separable prefix

This is not random. It is a regular grammar pattern.

Compare:

• Ich kaufe das Ticket ein.
• Sie stellt das Fahrrad ab.
• Der Rückgabeautomat bucht das Buch zurück.

The infinitive is:

• zurückbuchen

The past participle is:

• zurückgebucht

Example:

• Der Rückgabeautomat hat das Buch zurückgebucht.

That follows the usual pattern for many separable verbs:

• prefix + ge
  • verb stem

So:

• zurück
  • ge
    • bucht → zurückgebucht

The normal, neutral order is:

• Der Rückgabeautomat bucht das Buch zurück.

German can change word order for emphasis, but the conjugated verb still stays in the second position in a main clause:

• Das Buch bucht der Rückgabeautomat zurück.

That version is grammatical, but it sounds marked or contrastive, as if you are especially focusing on das Buch.

For learners, the standard order is the best one to use first:

• subject + verb + object + separable prefix

A rough guide is:

• RÜCK-gaa-buh-au-toh-maht

A few helpful points:

• ü is not like normal English oo. It is a front rounded vowel. If you know French, it is similar to u in tu.
• ck makes a short, crisp k sound.
• gabe has a long a sound.
• Automat is pronounced roughly ow-toh-maht, not like English automatic.

Also remember that German compound nouns are pronounced as one word, but you can still hear the parts inside them:

• Rückgabe
  • Automat