Szóstego grudnia spotykamy się u babci na kolacji.

Because Polish dates are normally expressed with:

• an ordinal number for the day
• the month name in the genitive case

So szóstego grudnia means on the sixth of December / December 6th.

The form szóstego is also in the genitive here. It agrees with an understood noun like dzień (day), so the full idea is roughly szóstego dnia grudnia, though in normal speech you just say szóstego grudnia.

Szósty grudzień is not how Polish dates are normally said.

Month names in dates usually appear in the genitive in Polish.

Examples:

• pierwszego maja — on the first of May
• dwunastego lipca — on the twelfth of July
• szóstego grudnia — on the sixth of December

The nominative form is grudzień, but in dates it changes to grudnia.

Because spotykać się is the normal Polish verb for to meet (each other).

Compare:

• spotykać kogoś — to meet someone
• spotykać się — to meet up / to meet each other

So:

• Spotykamy babcię = We meet grandma
• Spotykamy się u babci = We are meeting up at grandma’s place

In this sentence, się is necessary because the meaning is reciprocal: the people are meeting one another.

Grammatically, it is a present-tense form, but in Polish the present tense of an imperfective verb is often used for a planned future event.

So here:

• spotykamy się literally looks like we meet / we are meeting
• but in context it means we’re meeting or we’re getting together on that date

This is very natural in Polish, just like English We’re meeting at grandma’s on December 6th.

U + genitive is very commonly used in Polish to mean at someone’s place / at someone’s home / at someone’s place of business.

So:

• u babci = at grandma’s
• u mamy = at mom’s
• u lekarza = at the doctor’s

It does not literally mean inside grandma or anything like that; it is simply the normal Polish way to say at grandma’s place.

Because after u, Polish uses the genitive case.

The dictionary form is:

• babcia — grandma

But after u, it changes:

• u babci — at grandma’s

So this is a case change triggered by the preposition u.

These two forms mean different things.

• na kolacji = at dinner / during dinner
• na kolację = for dinner

In your sentence, spotykamy się u babci na kolacji means the meeting takes place for the occasion of dinner / at dinner.

A useful contrast:

• Jesteśmy na kolacji. — We are at dinner.
• Idziemy do babci na kolację. — We’re going to grandma’s for dinner.

So na kolacji emphasizes being at the dinner gathering itself, while na kolację often appears with motion, especially go / come for dinner.

Yes. That is very common.

You can say:

• szóstego grudnia
• 6 grudnia

Both are natural. The second is especially common in writing and everyday speech.

When read aloud, 6 grudnia is still understood as szóstego grudnia.

Because in Polish, names of months are normally written with lowercase letters, unlike in English.

So:

• grudzień
• maj
• lipiec

not capitalized, unless they begin a sentence.

This is standard Polish spelling.

Yes. Polish word order is more flexible than English, because the case endings show the grammatical relationships.

Your sentence:

• Szóstego grudnia spotykamy się u babci na kolacji.

Could also be:

• Spotykamy się u babci na kolacji szóstego grudnia.
• U babci spotykamy się na kolacji szóstego grudnia.

These versions are still understandable, but they change the focus slightly.

The original sentence sounds very natural if you want to start by giving the date.

It suggests a social meal occasion: the people are meeting for dinner / at dinnertime / at a dinner gathering.

It sounds more natural than just saying na obiedzie or na posiłku unless you specifically mean those things.

In this sentence, na kolacji gives the idea that the meeting is centered around dinner, not just that dinner happens to be present.

A rough guide is:

• szó — like shoo, but shorter
• ste — like steh
• go — like gaw or go, depending on accent and speech

Very roughly: SHOOS-teh-go

A few pronunciation points:

• sz sounds like English sh
• ó sounds like Polish u
• cz / ci / si / sz distinctions matter in Polish, so it helps to listen to native audio

The whole phrase szóstego grudnia can feel tricky at first because of the consonant clusters, so it is worth practicing slowly.