На собрании он попытался доказать, что его версия точнее моей.

Because Russian usually uses на with events and organized activities:

• на собрании = at the meeting
• на уроке = at class / in class
• на концерте = at the concert

Here собрание is treated as an event, not as a physical space you are "inside," so на is the normal choice.

It is prepositional singular.

The dictionary form is собрание. After на in the meaning of location or setting, it takes the prepositional case:

• собрание → на собрании

This -ии ending is normal for many neuter nouns ending in -ие.

Попытался is the masculine singular past tense of попытаться, meaning to try or to attempt.

It matches он, so the past tense is masculine:

• он попытался
• она попыталась
• они попытались

The -ся is part of the verb попытаться. Here it does not literally mean himself; it is just how this verb is formed.

Because доказать is perfective, and after попытаться Russian often uses a perfective infinitive to show the intended result:

• попытался доказать = tried to prove

This focuses on the goal: proving something.

If you said попытался доказывать, it would sound more like he tried to engage in the process of arguing/proving, with more emphasis on the ongoing activity rather than the result.

Что introduces the clause that contains what he tried to prove:

• он попытался доказать, что...
• he tried to prove that...

In English, that is sometimes omitted. In Russian, что is much more normally kept in this kind of sentence.

Because свой normally refers to the subject of its own clause.

In the clause что его версия точнее моей, the grammatical subject is версия. So своя версия would wrongly suggest something like its own version, which does not fit.

So Russian uses его to refer back to он from the main clause.

Точнее is the comparative form of точный, meaning more accurate or more precise.

Russian often forms comparatives as a single word:

• быстрый → быстрее
• важный → важнее
• точный → точнее

So:

• его версия точнее = his version is more accurate

Because Russian can use the genitive of comparison after a comparative form.

So:

• точнее моей = more accurate than mine
• full version: точнее моей версии

Here моей is genitive singular feminine, agreeing with the omitted noun версии.

If you used моя, that would be nominative, so it would not fit this pattern.

Yes.

Russian often leaves out a repeated noun when it is obvious from context. Since версия already appeared, моей alone is enough:

• его версия точнее моей
• literally: his version is more accurate than mine
• underlying full form: его версия точнее моей версии

This is very natural Russian.

Yes, that is also correct.

Russian has two common comparison patterns:

• comparative + genitive: точнее моей версии
• comparative + чем: точнее, чем моя версия

So these are both possible:

• его версия точнее моей
• его версия точнее, чем моя версия

The version with моей is more compact.

Because Russian usually omits the present-tense form of to be.

So Russian says:

• его версия точнее моей

Literally this looks like:

• his version more accurate than mine

But it means:

• his version is more accurate than mine

This is completely normal in Russian.