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I don't have any approach to it, just tried to understand. I wonder how it possible to learn a languge where the main rule is total arbitrariness.

I think the thing that make difference between cases is the sense not the form. The principal difference between the accusative and the genitive is that the accusative shows an affection of a subject...

Accusative. Have I passed the test? :)

http://www.evartist.narod.ru/text1/66.htm#%D0%B7_04[/quote]
But what difference in pattern between "Я не понял этого вопроса" and "Я не понял этого...

To Полуношник
In these phrases:
Я не понял этого человека.
Я вспоминаю брата.
What case there to you?

That's not only in negation. Likely a half of people say "я купил хлеба"
And this is not quite right to say that the genitive case is used instead of accusative, the sentences like "Я не понял этого...

As I notice there is wide using the genitive form of words in accusative case.
From yandex:
"Я не знал этой песни" - 253
"Я не знал эту песню" - 23
"Я не понял этого вопроса" - 308
"Я не...