Después de hablar con mi profesora, llegué a comprender la diferencia.

Because después is followed by the preposition de before an infinitive.

So in Spanish, you say:

• después de hablar = after speaking
• después de comer = after eating
• después de estudiar = after studying

You cannot normally say después hablar.

A useful pattern to remember is:

después de + infinitive

or

después de + noun

For example:

• Después de la clase, me fui. = After class, I left.
• Después de hablar con ella, lo entendí. = After speaking with her, I understood it.

It is in the infinitive because after después de, Spanish commonly uses the infinitive when the subject is the same as in the main clause.

In this sentence, the same person:

• spoke with the teacher
• later came to understand the difference

So Spanish uses:

Después de hablar con mi profesora...

This is similar to English After speaking with my teacher...

If Spanish needs to make the subject explicit or different, it may use a full clause instead. But with the same subject, después de + infinitive is very common and natural.

Llegar a + infinitive often means to eventually manage to, to come to, or to end up doing something.

So llegué a comprender means more than simple I understood. It suggests a process:

• at first, the speaker did not fully understand
• then, after some explanation or reflection
• they finally came to understand it

So it has a sense of gradual achievement or eventual realization.

Compare:

• Comprendí la diferencia. = I understood the difference.
• Llegué a comprender la diferencia. = I came to understand the difference / I eventually understood the difference.

The second one sounds more gradual and emphatic.

Llegué is the preterite, which presents the action as completed.

Here, the idea is that after speaking with the teacher, there was a completed result: the speaker came to understand the difference.

So llegué a comprender fits well because it describes a finished change or achievement.

If you used llegaba, that would be the imperfect, which usually describes ongoing, repeated, background, or incomplete actions. That would not fit as naturally here.

So:

• llegué a comprender = I came to understand / I eventually understood
• llegaba a comprender = I was coming to understand / I used to come to understand, depending on context

In this sentence, the preterite is the natural choice.

The a is part of the construction llegar a + infinitive.

It is not the personal a, and it does not mean to in a simple movement sense here. Instead, it belongs to a fixed verbal expression.

Examples:

• Llegó a ser médico. = He/She became a doctor.
• No llego a entenderlo. = I can’t quite understand it.
• Llegaron a pensar que era verdad. = They came to think it was true.

So in your sentence:

llegué a comprender = I came to understand

It is best learned as a chunk: llegar a + infinitive.

Both comprender and entender can mean to understand, and in many situations they are interchangeable.

However, comprender can sometimes sound a little more formal, thoughtful, or complete. In a sentence like this, it fits nicely because the speaker is talking about reaching a deeper understanding.

So:

• entender = understand
• comprender = understand, often with a slightly fuller or more formal tone

That said, Después de hablar con mi profesora, llegué a entender la diferencia is also grammatical and natural.

The difference is mostly one of style and nuance, not basic meaning.

Because profesora refers to a female teacher.

In Spanish, many nouns for people change form depending on gender:

• profesor = male teacher
• profesora = female teacher

Since the sentence says mi profesora, the speaker is referring to my female teacher.

Also notice that mi does not change here:

• mi profesor
• mi profesora

The possessive mi works for both masculine and feminine singular nouns.

The comma separates the introductory phrase from the main clause.

The structure is:

• Después de hablar con mi profesora, = introductory time phrase
• llegué a comprender la diferencia. = main clause

This comma is very common and helps readability. In English, you would often do the same:

After speaking with my teacher, I came to understand the difference.

In short, it is not changing the meaning; it is just marking the pause between the introductory phrase and the main statement.

Spanish often uses the definite article where English might omit it.

Here, la diferencia means the difference, referring to a specific difference already known from context.

So Spanish prefers:

• comprender la diferencia
• entender la idea
• explicar el problema

rather than dropping the article.

If you said just comprender diferencia, it would sound incomplete or unnatural in normal Spanish.

Yes. Spanish word order is flexible, and you could say:

Llegué a comprender la diferencia después de hablar con mi profesora.

This means the same thing.

The difference is mainly about emphasis:

• Después de hablar con mi profesora, llegué a comprender la diferencia.
  This emphasizes the time/background first.
• Llegué a comprender la diferencia después de hablar con mi profesora.
  This emphasizes the main result first.

Both are natural.

Because hablar con means to speak with / to talk to someone.

Very common patterns are:

• hablar con alguien = speak with someone
• hablar de algo = talk about something
• hablar sobre algo = talk about something

So:

• hablar con mi profesora = speak with my teacher
• hablar de la diferencia = talk about the difference

In your sentence, con shows who the conversation was with.

Yes, you could.

Tras also means after, and tras hablar con mi profesora is correct. However, después de is usually more common and neutral in everyday speech.

Compare:

• Después de hablar con mi profesora, llegué a comprender la diferencia.
• Tras hablar con mi profesora, llegué a comprender la diferencia.

The second can sound slightly more formal or written, but both are good Spanish.

Yes, it is completely natural in Spain Spanish.

Nothing in the sentence sounds un-Spanish or odd for Spain. In fact, the whole sentence is standard and would be understood everywhere in the Spanish-speaking world.

A speaker from Spain might also say similar things like:

• Después de hablar con la profesora, por fin entendí la diferencia.
• Tras hablar con mi profesora, acabé comprendiendo la diferencia.

But your original sentence is already perfectly natural and correct.