Magistra dicit Luciam hanc sententiam perfecte interpretari.

Because Latin is using an indirect statement after dicit. In this construction, the person doing the action inside the reported statement goes into the accusative, and the verb of that reported statement goes into the infinitive.

So in:

Magistra dicit Luciam hanc sententiam perfecte interpretari

• Magistra = the subject of dicit
• Luciam = the subject of interpretari, but in the accusative because of indirect statement

In English, we often use that:

• The teacher says that Lucia interprets this sentence perfectly.

Latin does not use that here. It uses accusative + infinitive instead.

Because it is the verb inside the indirect statement introduced by dicit.

After verbs of saying, thinking, knowing, hearing, and so on, Latin very often uses:

• accusative subject
• infinitive verb

So:

• Luciam = accusative subject
• interpretari = infinitive verb

This is one of the most important Latin constructions to learn.

It looks passive, but here it is actually a deponent verb.

Interpretor, interpretari, interpretatus sum is a deponent verb, which means:

• it has passive forms
• but an active meaning

So interpretari means to interpret, not to be interpreted.

That is why the sentence means that Lucia is doing the interpreting.

It is an accusative-and-infinitive construction, often abbreviated AcI.

This is the normal Latin way to express indirect statement.

Structure here:

• dicit = the main verb, says
• Luciam = accusative subject of the indirect statement
• interpretari = infinitive verb of the indirect statement
• hanc sententiam = object of interpretari
• perfecte = adverb modifying interpretari

So the whole reported idea is:

• Luciam hanc sententiam perfecte interpretari

Because it is the direct object of interpretari.

Lucia is the one doing the action of interpreting, and this sentence is what she is interpreting.

So the two accusatives have different jobs:

• Luciam = subject of the infinitive in indirect statement
• hanc sententiam = direct object of the infinitive

This is very common in Latin and can feel unusual to English speakers, because English usually does not mark these roles by case so clearly.

Hanc is the feminine singular accusative form of hic, haec, hoc, meaning this.

It agrees with sententiam in:

• gender: feminine
• number: singular
• case: accusative

So:

• sententia is a feminine noun
• its accusative singular is sententiam
• therefore the matching form of hic must be hanc

That is why Latin has hanc sententiam = this sentence.

Perfecte is an adverb, and it modifies interpretari.

It tells us how Lucia interprets the sentence:

• perfecte = perfectly

So it does not describe Luciam or sententiam. It describes the action of interpreting.

Because magistra is the subject of the main verb dicit.

So:

• magistra = the teacher
• dicit = says

This is the main clause:

• Magistra dicit = The teacher says

Everything after that is the content of what the teacher says.

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

For example, the following would still mean essentially the same thing:

• Luciam magistra hanc sententiam perfecte interpretari dicit
• Magistra Luciam perfecte hanc sententiam interpretari dicit
• Hanc sententiam Luciam magistra perfecte interpretari dicit

However, word order can affect emphasis. The given sentence is fairly straightforward and easy to read:

• main subject and verb first: Magistra dicit
• then the indirect statement: Luciam hanc sententiam perfecte interpretari

Because classical Latin usually expresses this idea with the accusative-and-infinitive construction instead of a conjunction like that.

English says:

• The teacher says that Lucia interprets this sentence perfectly.

Latin says:

• Magistra dicit Luciam hanc sententiam perfecte interpretari.

So the idea of that is understood from the grammar itself.

Because Luciam is the accusative subject of the infinitive interpretari.

The sentence has two layers:

1. Main statement: Magistra dicit = The teacher says
2. Reported statement: Luciam ... interpretari = Lucia ... interprets

So:

• magistra performs dicit
• Luciam performs interpretari

This is exactly how indirect statement works in Latin.

Not with this verb in the way it is used here. Since interpretor is deponent, its forms look passive but normally have an active meaning.

So:

• interpretari = to interpret

If Latin wanted to say to be interpreted, it would usually use a different wording, not this deponent infinitive understood as passive.

It is the present infinitive, and in indirect statement it usually shows action happening at the same time as the main verb.

So:

• dicit = she says
• interpretari = to be interpreting / interprets, contemporaneous with says

In smoother English, we usually translate it simply as:

• The teacher says that Lucia interprets this sentence perfectly.

If Latin wanted to show an earlier or later time in the indirect statement, it would use a different infinitive form.