Шестого июня у нас будет встреча в парке.

Because Russian dates usually use the genitive case.

In calendar dates, the day number is put in the genitive, and the month is also in the genitive:

• первое июня = June first? Actually, when standing alone as a date, Russian normally says первое июня only in nominative-style citation or in special contexts, but in sentences with an implied on, the standard form is:
• первого июня = on the first of June
• шестого июня = on the sixth of June
• двадцать пятого декабря = on the twenty-fifth of December

So in Шестого июня у нас будет встреча в парке, шестого июня means on June 6th.

That is just the standard Russian pattern for dates in sentences.

• шестого = genitive form of шестое
• июня = genitive form of июнь

Russian treats dates as a fixed construction:

• пятого мая
• десятого августа
• тридцать первого января

English uses on June 6th, but Russian usually expresses this with the genitive date phrase and often does not need a separate word for on.

Yes, in terms of meaning.

Russian often omits a separate preposition where English uses on with dates. So:

• Шестого июня = On June 6th

You do not normally need в or another preposition before the date here.

Literally, у нас can mean something like at our place, with us, or among us, depending on context. In this sentence, it is best understood as:

• we have
• there will be for us
• on our side / in our group / at our place

So у нас будет встреча means something like:

• we will have a meeting
• there will be a meeting for us
• we’ve got a meeting

This is a very common Russian structure:

• У меня есть книга. = I have a book.
• У нас будет урок. = We will have a lesson.
• У них завтра экзамен. = They have an exam tomorrow.

So yes, the literal idea is connected to at us / by us, but the natural English translation is usually just we have.

Because Russian often expresses there will be or we will have with быть.

Here:

• будет = will be
• встреча = meeting

So у нас будет встреча literally means with us there will be a meeting, which naturally becomes we will have a meeting.

Russian does have other ways to say take place or happen, such as:

• состоится = will take place
• произойдёт = will happen

But будет встреча is simple, neutral, and very common.

Because it is the grammatical subject of будет.

In the structure у нас будет встреча, the thing that will be is встреча. So встреча stays in the nominative singular.

Compare:

• Будет встреча. = There will be a meeting.
• Будет концерт. = There will be a concert.
• Будет проблема. = There will be a problem.

Even though English may translate this as we will have a meeting, Russian grammar is really built around a meeting will be.

Yes, Russian word order is fairly flexible.

This version is natural because it moves from time to who/for whom to what will happen to place:

• Шестого июня = time
• у нас = for us / we have
• будет встреча = there will be a meeting
• в парке = in the park

Other possible word orders include:

• У нас будет встреча в парке шестого июня.
• В парке у нас будет встреча шестого июня.
• Шестого июня встреча у нас будет в парке.

These may sound slightly different in emphasis, but they are grammatically possible. The original sentence is neutral and natural.

Because в парке answers where?, not to where?

• в парк = into the park / to the park after motion
• в парке = in the park for location

Here the meeting is located in the park, so Russian uses the prepositional case:

• парк → в парке

Compare:

• Мы идём в парк. = We are going to the park.
• Мы гуляем в парке. = We are walking in the park.
• Встреча будет в парке. = The meeting will be in the park.

Russian has no articles like a or the.

So встреча by itself can mean:

• a meeting
• the meeting

The exact meaning depends on context.

In this sentence, English would most naturally say a meeting if it is being mentioned for the first time:

• On June 6th, we will have a meeting in the park.

If the meeting is already known, English might use the meeting, but Russian still just says встреча.

Yes. Встреча can mean several related things:

• a meeting
• an appointment
• a get-together
• an encounter

The exact sense depends on context.

For example:

• деловая встреча = business meeting
• встреча с друзьями = meeting with friends
• случайная встреча = chance encounter

In your sentence, встреча в парке could be a planned meetup, not necessarily a very formal office-style meeting.

You could move в парке closer to the end for stronger focus, or use intonation in speech. The original already ends with в парке, which naturally gives it some emphasis.

Possible versions:

• Шестого июня у нас будет встреча в парке.
  Neutral, natural.

• Шестого июня у нас в парке будет встреча.
  Slightly highlights that it is at our park / in the park depending on context.

• Шестого июня у нас будет встреча именно в парке.
  Strong emphasis: specifically in the park.

Russian often uses word order and particles like именно to show emphasis.

Yes, absolutely.

That is also natural Russian. It just places the date later in the sentence:

• У нас будет встреча шестого июня в парке.

This still means the same thing. Russian allows this because case endings show the grammatical relationships, so word order can shift more freely than in English.

The original sentence puts the date first because time expressions often come early when setting the scene.

A rough pronunciation guide is:

• шестого ≈ shi-STOH-vuh
• июня ≈ ee-YOO-nyuh

A few important things to notice:

• Unstressed о is often pronounced more like uh
• ю in июня sounds like yoo
• The stress is:
  • шесто́го
  • ию́ня

So the whole phrase sounds approximately like:

• shi-STOH-vuh ee-YOO-nyuh

This is only an approximation, but it is close enough to help an English speaker get started.