Knew/know

Neither!

rajesh jainI didn't able to know/knew that you were from Finland?

"Did not", which is a modal, is always followed by a verb. "Able" is an adjective which is always preceded by a form of the "be" verb.

" I didn't able " is an illegal grammatical structure.

thanks for your help and what about these-
I wasn't able to know that u were from finland. or,
how were you not able to know that he was from finland.

rajesh jainI wasn't able to know that you were from Finland. or, How were you not able to know that he was from Finland?

Now they are okay.

I wasn't able to know that you

Don't you 'I wasn't able to know that you are from Finland' prefer?
It makes more sense..

I wasn't able to know.

"I wasn't able to know" seems a little odd to me. Usually you either know something or you don't know it; it's not a question of "being able to know." Do you mean "I had no way of knowing ...?" That means "I had no opportunity to learn"something.

In know in form, it is correct. but semantically speaking it sounded odd to me too.
It sounds correct if it were : I wasn't able to "tell....."

rajesh jainWhich is correct?I didn't able to know/knew that you were from Finland?

I think you are just trying to say, "I didn't know you were from Finland".
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In any case note that an infinitive is invariable. You can't have different inflections for an infinitive. For example, in the case of know, the i

Thanks for your help.It is clear now.

the sentence is running in past indefinite and whenever we make negative sentences in past ind we never use 2nd or 3rd form with 'did' we only use first form with did because did is already a 2nd form of do....