Discipuli scriptorem viventem libenter audiunt.

Because discipuli is nominative plural, and the verb audiunt is also plural: they hear / they listen.

A beginner may notice that discipuli could also, in some contexts, be genitive singular, meaning of the student. But here that would not make good sense syntactically. The sentence needs a subject for audiunt, and discipuli fits perfectly as the students.

So here:

• discipuli = students, nominative plural, the subject

Because scriptorem is accusative singular, the form used for the direct object.

The students are doing the action, and the writer is the one being heard or listened to. So:

• discipuli = the students
• scriptorem = the writer / author

The base form is scriptor. Its accusative singular is scriptorem.

Viventem is the present active participle of vivere, meaning living or alive.

A participle is a verbal adjective. That means it comes from a verb, but it behaves like an adjective and describes a noun.

So here viventem describes scriptorem:

• scriptorem viventem = the living author or the author who is alive

Because it agrees with scriptorem.

In Latin, adjectives and participles agree with the nouns they describe in:

• gender
• number
• case

Since scriptorem is masculine singular accusative, viventem must also be masculine singular accusative.

So the pair matches:

• scriptorem = accusative singular
• viventem = accusative singular

This agreement is what shows that viventem describes scriptorem.

It can feel like both, because it is a participle.

In this sentence, it is most naturally understood as an adjective-like description: the living author. But it still has a verbal origin from vivere, to live.

A fuller paraphrase would be:

• scriptorem viventem = the author who is living
• more idiomatically in English: the living author

So Latin is using a participle where English might use either an adjective or a relative clause.

Libenter is an adverb meaning gladly, willingly, or with pleasure.

It modifies the verb audiunt, telling us how the students listen.

So the sense is:

• They gladly listen
• They listen with pleasure

It does not describe the author; it describes the action.

Latin audire can cover both ideas that English often separates into hear and listen to, depending on context.

So:

• scriptorem audiunt can mean they hear the author
• and often, in a context like this, more naturally they listen to the author

Latin does not need a separate preposition here. English says listen to someone, but Latin simply uses the direct object with audire.

Quite a lot.

Audiunt is:

• present tense
• active voice
• indicative mood
• third person plural

So it means they hear or they are listening.

It comes from audio, audire, a fourth-conjugation verb. That is why the form is audiunt.

Because classical Latin has no articles.

Latin does not normally have separate words for the, a, or an. Whether a noun is definite or indefinite is usually understood from context.

So:

• discipuli can mean students or the students
• scriptorem can mean a writer, the writer, an author, or the author

The meaning shown to the learner tells you which English wording fits best, but the Latin itself does not include an article.

The word order is fairly flexible because the endings show the grammar.

So this sentence could be rearranged without changing the basic meaning, for example:

• Discipuli scriptorem viventem libenter audiunt
• Discipuli libenter scriptorem viventem audiunt
• Scriptorem viventem discipuli libenter audiunt

The endings still show:

• discipuli = subject
• scriptorem viventem = object phrase
• audiunt = verb

That said, word order can change emphasis. The given order is natural and clear.