El profesor, por su parte, aceptó el plan.

Por su parte is a set expression meaning for his part, as for him, or on his side.

In this sentence, it shows contrast or a shift of focus:

• someone else may have done or said something before
• the teacher/professor, for his part, accepted the plan

It often helps organize information, especially when talking about different people’s reactions.

Because por su parte is being used as a parenthetical expression, not as an essential part of the sentence structure.

The core sentence is: El profesor aceptó el plan.

The phrase por su parte is added to give extra context, so it is set off with commas: El profesor, por su parte, aceptó el plan.

In English, this is similar to: The professor, for his part, accepted the plan.

In Spanish, it is very common to use the definite article with nouns where English might not.

Here, el profesor means the professor or the teacher, referring to a specific person already known from the context.

Just profesor by itself is less natural in this kind of sentence unless you are using it as a form of address, for example: Profesor, tengo una pregunta.
= Professor/Teacher, I have a question.

It can mean either, depending on context.

In Spanish, profesor is commonly used for a teacher at school or secondary school, not only for a university professor. So for an English speaker, this word can be a little misleading.

Depending on context, El profesor could be translated as:

• the teacher
• the professor

In Spain, profesor is a very normal word for a teacher.

Aceptó is the third-person singular preterite form of aceptar.

That means:

• aceptar = to accept
• aceptó = he accepted, she accepted, or it accepted

It is used for a completed action in the past. So the sentence presents the acceptance as a finished event.

The accent mark shows both pronunciation and meaning.

• aceptó = he/she accepted (preterite)
• acepto = I accept or I do accept (present)

So the accent is important because it distinguishes two different forms.

It also tells you the stress falls on the last syllable: a-cep-TÓ

In standard Spanish, especially in many varieties, the preterite aceptó is used to describe a completed past action.

So:

• aceptó el plan = accepted the plan

You could also hear ha aceptado el plan in some contexts, especially in Spain, if the speaker connects the action more closely to the present. But aceptó is perfectly natural for simply narrating what happened.

So the choice here presents the action as a straightforward completed event in the past.

El plan is the direct object of the verb aceptó. It is the thing that was accepted.

So the structure is:

• El profesor = subject
• aceptó = verb
• el plan = direct object

Because it is a specific plan already known in context, Spanish uses el: accepted the plan

Yes, Spanish allows some flexibility.

For example, these are possible:

• El profesor, por su parte, aceptó el plan.
• Por su parte, el profesor aceptó el plan.

Both are natural. The version with por su parte in the middle sounds slightly more inserted or parenthetical. Putting it first gives it a little more emphasis.

The basic meaning stays the same.

Sometimes, yes, depending on context. It often introduces what one person did or said in contrast with someone else, so in natural English it may be translated in different ways, such as:

• for his part
• as for him
• meanwhile
• on his side

But its most literal value is about that person’s own part, position, or reaction.

In this sentence, for his part is probably the closest match.