Puella in arena ludit, et frater eius prope litus ambulat.

Latin does not have articles. There is no direct equivalent of the or a/an as a normal part of the language.

So puella can mean the girl or a girl, depending on context. The same is true for arena, frater, and litus.

Both puella and frater are in the nominative singular, because they are the subjects of their verbs.

• puella = the girl / a girl
• frater = the brother / a brother

In this sentence:

• puella is the subject of ludit
• frater eius is the subject of ambulat

Here in means in or on in the sense of location, so it takes the ablative case.

That is why we get:

• arena = ablative singular of arena, arenae

A useful rule is:

• in
  • ablative = in/on somewhere
• in
  • accusative = into somewhere

So in arena means in the arena or on the sand, not into the arena.

Prope is a preposition that takes the accusative case, so litus here is accusative singular.

The noun is:

• litus, litoris = shore, seashore, beach

Because litus is a neuter third-declension noun, its nominative singular and accusative singular look the same. So even though the form is litus, here it is accusative because prope requires it.

So:

• prope litus = near the shore

Eius means his, her, or its, depending on context. Here it means her, so frater eius means her brother.

Grammatically, eius is the genitive singular form of the pronoun is, ea, id.

You can think of frater eius literally as the brother of her, although in natural English we say her brother.

This is a very common question.

Suus, sua, suum is a reflexive possessive. It normally refers back to the subject of its own clause.

In the second clause, the subject is frater:

• frater eius prope litus ambulat

If Latin used suus here, it would normally point back to frater, not to puella. But the meaning is her brother, referring to the girl mentioned earlier, not his own brother.

So eius is used because the possessor is someone other than the subject of that clause.

Both are third person singular present active indicative verbs.

• ludit = he/she/it plays, is playing
• ambulat = he/she/it walks, is walking

More specifically:

• ludit comes from ludere
• ambulat comes from ambulare

Because the subjects are singular:

• puella → ludit
• frater → ambulat

It can mean either one.

The Latin present tense often covers both:

• simple present: plays
• progressive present: is playing

So Puella in arena ludit can mean:

• The girl plays in the arena
• The girl is playing in the arena

The exact sense depends on context.

The same applies to ambulat:

• walks
• is walking

Yes. Latin word order is much more flexible than English word order because the endings show the grammatical roles.

This sentence is:

• Puella in arena ludit, et frater eius prope litus ambulat.

That is a perfectly normal order, but Latin could move parts around for emphasis or style.

For example, Latin often places the verb later in the clause, as it does here:

• subject + phrase + verb

The basic meaning stays clear because:

• puella is nominative
• frater is nominative
• arena is ablative after in
• litus is accusative after prope

So word order matters less in Latin than in English.

Latin often does not need subject pronouns because the verb ending already tells you the person and number.

For example:

• ludit already means he/she/it plays
• ambulat already means he/she/it walks

In this sentence, the subjects are stated explicitly as nouns:

• puella
• frater eius

So there is no need to add pronouns like ea or is unless there is some special emphasis or contrast.

Et means and. It joins the two clauses:

• Puella in arena ludit
• frater eius prope litus ambulat

So the sentence is made of two linked statements:

• The girl is playing in the arena
• and her brother is walking near the shore

It is one of the most common Latin conjunctions.