Puella respondet se inscriptiones Romanas nunc facilius legere posse, quia antea inscriptiones Graecas viderit.

Because this is an indirect statement after respondet.

In Latin, the subject of an indirect statement goes into the accusative, and if that subject refers back to the subject of the main verb, Latin uses the reflexive pronoun se.

So here:

• puella respondet = the girl replies
• se ... posse = that she can ...

Because se refers back to puella, it means herself / she. If it referred to some other female person, Latin would use eam, not se.

Latin usually does not use a separate word like English that in indirect statements.

Instead, it uses the accusative-and-infinitive construction:

• accusative subject: se
• infinitive verb: posse

So:

• Puella respondet se ... posse
  = The girl replies that she can ...

This is one of the most important differences between English and Latin syntax.

Because posse means to be able, and it normally takes another infinitive to complete its meaning.

So:

• legere = to read
• posse = to be able
• legere posse = to be able to read

In English we say can read or to be able to read. Latin expresses that with posse + infinitive.

Because indirect statement requires an infinitive, not a finite verb.

If the direct idea were something like:

• Possum inscriptiones Romanas legere
  = I can read Roman inscriptions

then in indirect statement it becomes:

• se inscriptiones Romanas legere posse
  = that she can read Roman inscriptions

So potest / possum becomes posse in this construction.

Facilius is the comparative adverb, meaning more easily.

It modifies the verb legere:

• facilius legere = to read more easily

By contrast:

• facile or faciliter = easily
• facilius = more easily

So the sentence is not just saying she reads them easily; it says she reads them more easily now.

The comparison is implied, not stated with a separate than phrase.

Here nunc and antea make the comparison clear:

• nunc = now
• antea = earlier / before

So nunc facilius naturally means:

• more easily now than before

It does not have to mean more easily than Greek inscriptions. The time words strongly suggest comparison with an earlier stage.

They are adjectives agreeing with inscriptiones.

Inscriptiones is:

• feminine
• plural
• accusative

So its adjectives must match:

• inscriptiones Romanas
• inscriptiones Graecas

Both phrases are direct objects:

• inscriptiones Romanas is the object of legere
• inscriptiones Graecas is the object of viderit

This is standard Latin adjective agreement: same gender, number, and case as the noun.

Because the quia clause gives the girl’s own explanation, and it is part of what is being reported.

In Latin, subordinate clauses inside reported speech often go into the subjunctive. So:

• quia ... viderit = because, as she says / as her explanation goes, she had seen ...

This makes the reason belong to the reported statement, not necessarily to the narrator’s own independent assertion.

So the subjunctive here is a very natural way to show reported reason.

Viderit is perfect subjunctive.

Here it shows an action that happened before the main present-time idea:

• she replies now
• because she had earlier seen Greek inscriptions

So a natural English translation is:

• because she had earlier seen Greek inscriptions

A useful grammar point here is sequence of tenses:

• main verb in present: respondet
• prior action in subordinate subjunctive clause: viderit

If the main verb were past, Latin would often use a pluperfect subjunctive instead, for example vidisset.

Because antea adds the idea lexically and emphatically.

The tense already shows that the seeing happened earlier, but antea makes that relationship explicit:

• nunc = now
• antea = earlier / before

That pairing is elegant and clear. Latin often uses both a tense and a time word together.

Latin word order is fairly flexible.

Both legere posse and posse legere are possible. Here legere posse is a very normal order. Latin often places posse at the end of the indirect statement, which gives a neat closing effect.

What matters most is not the order by itself, but the grammatical signals:

• se = subject of the infinitive
• inscriptiones Romanas = object
• legere posse = to be able to read

So the order helps style and emphasis, but the endings carry the grammar.

Yes. Respondere can mean to answer or to reply, and like other verbs of speaking it can introduce indirect statement.

So:

• Puella respondet se ... posse

is perfectly standard Latin for:

• The girl replies that she can ...

It works much like dicit, ait, or negat in this respect.