Он помнит наше пари.

Because пари is a neuter noun in Russian, so any adjective or possessive pronoun agreeing with it must also be neuter singular: наше.

This can feel odd because пари ends in -и, which does not look like a typical neuter noun. But пари is a borrowed, indeclinable noun, and its gender is neuter.

So:

• наш = masculine
• наша = feminine
• наше = neuter

That is why you get наше пари.

It is in the accusative case, because it is the direct object of помнит: he remembers what? — наше пари.

However, both words look unchanged:

• наше has the same form in nominative and accusative neuter singular
• пари is indeclinable, so it does not change form

So even though the phrase is accusative here, it looks exactly like the dictionary form.

Because пари is an indeclinable noun. That means it keeps the same form in all cases.

So you can get forms like:

• наше пари
• о нашем пари
• к этому пари

The surrounding words may change, but пари itself stays the same.

This is common with some borrowed nouns in Russian.

Помнит is the 3rd person singular present tense form of помнить, meaning to remember.

So:

• я помню = I remember
• ты помнишь = you remember
• он/она помнит = he/she remembers

In this sentence, он помнит means he remembers.

Yes, Russian can often omit the subject pronoun if it is clear from context.

So Помнит наше пари can be possible in the right context, but Он помнит наше пари is more neutral and explicit.

Including он can:

• make the sentence clearer
• add contrast, as in He remembers our bet
• sound more complete when the sentence stands alone

Also, the verb form помнит tells you it is 3rd person singular, but not whether the subject is he, she, or it, so он removes ambiguity.

Because помнить takes a direct object in Russian.

English often says remember something, and Russian works the same way here:

• помнить что? = to remember what?

So:

• Он помнит наше пари. = He remembers our bet.

You would not normally say помнит о нашем пари in this basic sense.

There is a phrase помнить о ком-то / о чём-то, but that has a slightly different nuance: to keep someone/something in mind, not forget about someone/something. In this sentence, simple direct-object помнить is the natural choice.

This is a very common question.

• помнить = to remember, to have something in your memory
• вспоминать = to recall, to try to bring something back to mind

So:

• Он помнит наше пари = He remembers our bet.
• Он вспоминает наше пари = He is recalling our bet / trying to remember it.

Помнить describes a state.
Вспоминать describes the process of remembering.

It is a real Russian word, but it is a loanword, originally from French.

It means bet or wager, and because it is borrowed, it keeps an unusual shape for Russian:

• it ends in -и
• it is indeclinable
• it is treated as neuter

That is why the phrase looks a little unusual compared with more typical Russian nouns.

Yes. Russian word order is flexible, and changing it usually changes focus or emphasis, not the basic meaning.

For example:

• Он помнит наше пари. = neutral word order
• Наше пари он помнит. = emphasis on our bet
• Помнит он наше пари. = can sound contrastive or stylistically marked, depending on context

The most neutral version for a standalone sentence is the one you have: Он помнит наше пари.

The main stress is:

• он
• по́мнит
• на́ше
• пари́

So the whole sentence is pronounced roughly: on POHM-neet NAH-she pah-REE

Two stress points that learners often want to note:

• по́мнит — stress on the first syllable
• пари́ — stress on the last syllable