Discipula rogat quomodo ad scholam pervenire possit, et magistra ei viam ostendit.

Because both are first-declension feminine nouns in the nominative singular, the form used for the subject of the verb.

• discipula = the female student / schoolgirl
• magistra = the female teacher

In this sentence, each one is the subject of its own verb:

• Discipula rogat = the student asks
• magistra ... ostendit = the teacher shows

So the matching -a ending does not mean they are doing the same job in the sentence at the same time; it just means they are both singular feminine subjects.

Rogat is third person singular, present active indicative of rogare.

So it means he/she asks or is asking, depending on context. Here the subject is discipula, so it means the student asks.

A native English speaker often expects a separate word for she, but Latin usually does not need one, because the verb ending already tells you the person and number.

Quomodo means how.

It introduces an indirect question:

• quomodo ad scholam pervenire possit = how she can get to school

This is not a direct question like Quomodo ad scholam pervenire potest?
Instead, it is a question reported inside a larger sentence: The student asks how...

That is why the clause behaves a little differently grammatically.

Because quomodo ... possit is an indirect question, and in Latin indirect questions normally take the subjunctive.

So:

• potest = indicative, she can
• possit = subjunctive, used here because it depends on rogat

This is one of the most important patterns in Latin syntax:

• direct question: Quomodo ... potest?
• indirect question: rogat quomodo ... possit

Because possum is commonly followed by an infinitive.

So:

• pervenire possit = may be able to arrive / can get
• literally, something like may be able to reach

This is the same basic pattern as in English:

• can go
• can reach
• is able to arrive

Latin uses:

• potest/pervenire
• possit/pervenire

So the infinitive pervenire depends on possit.

The subject is understood to be the same person as discipula.

Latin often leaves subject pronouns unstated when the meaning is clear from context. Here the clause means:

• how she might be able to get to school

Latin does not need to say ea here, because it is obvious that the student is asking about her own route.

So the understood subject of possit is the student.

Because it follows ad, which takes the accusative when it means to or toward.

So:

• ad scholam = to the school

This is the normal way to express motion toward a place.

A very common Latin pattern is:

• ad
  • accusative = to / toward

So scholam is accusative singular of schola.

Because ad scholam pervenire is a natural way to say to arrive at / get to school.

The verb pervenire means to come through to, to arrive at, or to reach. Latin often uses it with ad plus the accusative to mark the destination.

So:

• ad scholam pervenire = to get to school

An English speaker may want to translate word for word, but it is better to learn the whole phrase as a unit.

Ei is the dative singular of the pronoun is, ea, id.

Here it means to her:

• magistra ei viam ostendit = the teacher shows her the way

The dative is used for the indirect object, the person to whom something is given, said, shown, and so on.

So in this clause:

• viam = the thing shown
• ei = the person to whom it is shown

Because viam is the direct object of ostendit.

• ostendere = to show
• viam ostendere = to show the way

So the teacher shows what?
She shows the way. That makes viam accusative singular.

This gives us a nice contrast:

• ei = indirect object, to her
• viam = direct object, the way

Because Latin has no definite or indefinite article.

So a noun like discipula can mean:

• a student
• the student

The context tells you which is more natural in English.

The same is true for:

• magistra = a teacher / the teacher
• viam = a way / the way
• scholam = a school / the school

When translating into English, you add a or the as needed, but Latin itself does not use separate article words.

Because the whole sentence is not a direct question. It is a statement about someone asking a question.

So:

• direct question: Quomodo ad scholam pervenire possum?
• indirect question: Discipula rogat quomodo ad scholam pervenire possit.

In the sentence you have, quomodo ... possit is a question in meaning, but grammatically it is embedded inside a larger statement.

The word order matters for emphasis and style, but Latin word order is much freer than English word order because case endings show the grammatical roles.

Here the sentence is arranged quite naturally:

• Discipula rogat
• quomodo ad scholam pervenire possit
• et magistra ei viam ostendit

Even if some words were moved around, the endings would still tell you what belongs where. For example, ei is still dative and viam is still accusative no matter where they appear.

So English relies heavily on word order; Latin relies much more on endings.