Magistra rogat uter discipulus hanc sententiam facilius intellegat.

It has two parts:

• Magistra rogat = The teacher asks
• uter discipulus hanc sententiam facilius intellegat = an indirect question, literally which student understands this sentence more easily

So the whole sentence means something like:

The teacher asks which student understands this sentence more easily.

The verb rogat introduces the question, and everything after it is the content of what is being asked.

Uter means which of two?

That is the key idea. Latin uses:

• uter = which of the two
• quis or qui = who? / which? more generally

So this sentence suggests that the teacher is choosing between two students, not asking about a larger group.

Also, uter agrees with discipulus:

• masculine
• singular
• nominative

because it goes with discipulus and functions as the subject of intellegat.

Discipulus is nominative singular.

It is nominative because it is the subject of intellegat:

• uter discipulus ... intellegat = which student ... understands

Even though this whole clause depends on rogat, the subject of the embedded verb is still in the nominative.

Because this is an indirect question.

In Latin, indirect questions regularly take the subjunctive. So after rogat, Latin does not say:

• uter discipulus ... intellegit

but rather:

• uter discipulus ... intellegat

This is one of the most important patterns to learn:

• direct question: Quis hoc intellegit? = Who understands this?
• indirect question: Rogat quis hoc intellegat. = He asks who understands this.

So intellegat is not expressing doubt in the English sense; it is there because Latin grammar requires the subjunctive in indirect questions.

Intellegat is present subjunctive active, third person singular.

Here it usually corresponds to an English present sense:

• which student understands this sentence more easily

Because it depends on a present main verb (rogat), the present subjunctive is natural here.

Hanc sententiam is accusative singular feminine.

• hanc = this (accusative feminine singular)
• sententiam = sentence / statement (accusative singular)

It is accusative because it is the direct object of intellegat:

• intellegat hanc sententiam = understands this sentence

The demonstrative hanc agrees with sententiam in gender, number, and case.

Facilius is a comparative adverb, meaning more easily.

It modifies intellegat:

• hanc sententiam facilius intellegat = understands this sentence more easily

It is adverbial, not adjectival, so it does not describe the student; it describes the manner of understanding.

Compare:

• facilis = easy (adjective)
• facilius = more easily (comparative adverb)

Latin often leaves that unstated when the comparison is obvious from context.

Here facilius probably implies something like:

• more easily than the other student
• or more easily than someone else
• or more easily than before / than usual, depending on context

Because uter means which of two, the most natural interpretation is:

which of the two students understands this sentence more easily than the other

But Latin does not need to spell that out explicitly.

Because rogat here introduces a question, not an accusative-and-infinitive statement.

Latin uses different constructions for different kinds of reported content:

• reported statement: often accusative + infinitive
• indirect question: interrogative word + subjunctive

So after rogat, when the content is a question like which student?, Latin uses:

• uter discipulus ... intellegat

not an infinitive construction.

Yes. Rogo, rogare can introduce both direct and indirect questions.

So:

• Magistra rogat = The teacher asks
• followed by the indirect question: uter discipulus hanc sententiam facilius intellegat

This is a normal and straightforward use.

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

Here the order is:

• Magistra = subject of the main verb
• rogat = main verb
• uter discipulus = subject phrase of the indirect question
• hanc sententiam = object
• facilius = adverb
• intellegat = verb of the indirect question

A very literal English arrangement would be:

The teacher asks which student this sentence more easily understands.

That sounds odd in English, but it is perfectly natural in Latin. Latin often places the verb at the end of its clause, especially in subordinate clauses like this one.

You may see both spellings in different books:

• intellegat
• intelligat

Both represent the same verb, intellego / intelligo, understand. Many modern editions prefer intelleg-, which reflects the connection with lego in spelling, but learners commonly encounter both.

So if you have seen intelligit or intelligat elsewhere, do not be confused: it is the same word.

Usually no.

Uter specifically asks which of two. If the teacher were choosing among a larger group, Latin would more naturally use something like quis or qui instead, depending on the exact construction.

So uter discipulus strongly hints that there are two students under consideration.