Die Rückgabe ist möglich.

Because Rückgabe is a noun, and in German all nouns are capitalized.

In this sentence:

• die Rückgabe = the return / return
• ist = is
• möglich = possible

So the capitalization is not special to this word; it is the normal German rule for nouns.

Die is the definite article for the noun Rückgabe.

Here, Rückgabe is:

• feminine
• singular
• in the nominative case because it is the subject of the sentence

So:

• die Rückgabe = the return

A learner often expects article choice to match natural gender, but many German nouns for things and ideas also have grammatical gender. You simply have to learn Rückgabe as a feminine noun: die Rückgabe.

It is in the nominative case.

That is because die Rückgabe is the subject of the sentence:

• Die Rückgabe = the thing being talked about
• ist möglich = is possible

So the structure is:

• subject: Die Rückgabe
• verb: ist
• predicate adjective: möglich

Because Rückgabe is singular.

• die Rückgabe = singular
• therefore: ist

If the subject were plural, you would use sind:

• Die Rückgaben sind möglich.

But in German, this kind of statement is very often made with a singular abstract noun, even when English might naturally say something like returns are possible.

Yes, möglich is an adjective.

It has no ending here because it is being used predicatively, that is, after the verb sein.

Compare:

• Die Rückgabe ist möglich.
  Here möglich comes after ist, so it stays in its basic form.

But before a noun, an adjective would take an ending:

• eine mögliche Rückgabe

So:

• after sein: möglich
• before a noun: mögliche, möglichen, etc., depending on case and article

Rückgabe is a noun related to the verb zurückgeben, which means to give back or to return something.

You can think of it like this:

• zurückgeben = to return / to give back
• die Rückgabe = the return / the act of returning

This is very common in German: a verb and a related noun are often closely connected.

So if a shop says:

• Die Rückgabe ist möglich.

it means that returning the item is possible.

German often uses a more formal, compact style with nouns and adjectives, especially in notices, policies, or customer-service language.

So:

• Die Rückgabe ist möglich. = formal, neutral, policy-style wording

A more everyday way to express a similar idea could be:

• Man kann den Artikel zurückgeben. = You can return the item.
• Sie können den Artikel zurückgeben. = You can return the item. (formal you)

The version with Rückgabe sounds more like something you might read on a sign, website, receipt, or store policy.

Yes. That is very common on signs, labels, forms, and websites.

• Die Rückgabe ist möglich. = full sentence
• Rückgabe möglich. = shortened notice style

German often drops articles and even the verb in headlines or signs when the meaning is still clear.

So both are possible, but they have a different feel:

• Die Rückgabe ist möglich. = complete sentence
• Rückgabe möglich. = brief sign/policy language

This is standard German main-clause word order:

• Die Rückgabe = first position
• ist = conjugated verb in second position
• möglich = complement at the end

So the pattern is:

• Subject + verb + complement

That makes this a very straightforward sentence for learners.

A simple pronunciation guide is:

• Die ≈ dee
• Rückgabe ≈ RUEK-gah-buh
• ist ≈ ist
• möglich ≈ MERG-likh or MURG-likh depending on accent

A few helpful points:

• ü in Rück- is a front rounded vowel. English does not have an exact match.
• ö in möglich also has no exact English equivalent.
• The ch in möglich is the softer German ich-sound, not a hard k sound.

If you want a rough learner-friendly version, you can think of the whole sentence as:

• dee RUEK-gah-buh ist MERG-likh

That will not be perfect, but it is a useful start.

The plural is die Rückgaben.

So you have:

• singular: die Rückgabe
• plural: die Rückgaben

However, in this kind of sentence, German often prefers the singular abstract noun:

• Die Rückgabe ist möglich.

Even if English might express the idea more naturally with a plural, German often does not need the plural here.