Junho é o mês em que a professora começa o segundo semestre.

In Portuguese, the names of months usually appear without an article when you are just naming them:

• Junho é... = June is...
• Janeiro é quente. = January is hot.

In some contexts, you may hear an article with months, especially in more specific or regional usage, but the normal basic pattern is no article.

O mês means the month. Portuguese often uses the definite article when identifying something specific:

• Junho é o mês... = June is the month...

If you said Junho é mês..., it would sound incomplete or unnatural here. The sentence is pointing to one specific month that matches the description, so o is needed.

Here, em que means in which.

So:

• o mês em que a professora começa o segundo semestre
• literally: the month in which the teacher starts the second semester

This is a very common structure in Portuguese:

• a cidade em que moro = the city where I live
• o dia em que cheguei = the day when I arrived

It combines:

• em = in
• que = which / that

Usually, no. In standard Portuguese, quando is generally used directly with time expressions, but after a noun like mês, em que sounds more natural and standard.

So this is good:

• Junho é o mês em que a professora começa o segundo semestre.

You may also hear:

• Junho é o mês que a professora começa o segundo semestre.

That can occur in informal speech, but em que is clearer and more standard.

Portuguese often uses the definite article before nouns more than English does. So:

• a professora = the teacher

Even when English might say just the teacher in a broad way, Portuguese naturally includes the article.

Compare:

• A professora chegou. = The teacher arrived.
• O aluno estudou. = The student studied.

Leaving out the article here would sound unnatural in normal Portuguese.

Começa is the 3rd person singular present of começar = to start / to begin.

It matches a professora, which is singular:

• eu começo = I start
• você / ela / a professora começa = you / she / the teacher starts

The sentence is stating a general fact, so the present tense is the natural choice:

• Junho é o mês em que a professora começa...
• June is the month when the teacher starts...

This means the second semester.

Breakdown:

• o = the
• segundo = second
• semestre = semester / half-year term

Portuguese normally uses the definite article here because it refers to a specific school term:

• o primeiro semestre = the first semester
• o segundo semestre = the second semester

Not always. Semestre literally means a six-month period, so it can be used in different contexts:

• school: o segundo semestre letivo = the second school semester
• business: no primeiro semestre do ano = in the first half of the year

In this sentence, because of a professora, the school-related meaning is the most likely one.

Yes. Começar can mean both to start and to begin.

So this sentence could be understood as:

• June is the month in which the teacher starts the second semester.
• June is the month in which the teacher begins the second semester.

Both are fine in English.

In em que, the word que is a relative pronoun. It links o mês to the rest of the clause.

Structure:

• o mês = the month
• em que a professora começa o segundo semestre = in which the teacher starts the second semester

So que helps introduce extra information about o mês.

Yes, it is completely natural.

The structure is:

• Junho = subject
• é = is
• o mês em que... = predicate/complement

Portuguese commonly defines something this way:

• Abril é o mês em que chove mais. = April is the month when it rains the most.
• Segunda-feira é o dia em que trabalho mais. = Monday is the day when I work the most.

So the sentence sounds standard and natural.

Yes, but usually by changing the structure a little. For example:

• É em junho que a professora começa o segundo semestre. = It is in June that the teacher starts the second semester.

Or:

• A professora começa o segundo semestre em junho. = The teacher starts the second semester in June.

These are very natural. But in the original structure with o mês, em que is the best fit.

A very literal breakdown would be:

• Junho = June
• é = is
• o mês = the month
• em que = in which
• a professora = the teacher
• começa = starts / begins
• o segundo semestre = the second semester

So literally:

June is the month in which the teacher starts the second semester.

That literal translation matches the Portuguese structure quite closely.