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James, is it possible for two men to know their common ancestor by checking their Y-DNA.I mean, can it be known for example how many generations their forefather use to live.

Yes and no.

The way genetic genealogy works is that a man's Y chromosome, which is passed from father to son, sometimes mutates. This mutation is not very significant except that because Y chromosomes can only be transferred from fathers to sons, these mutations allow one to build a rough "family tree of humanity".

These mutations are rare however, and between mutations there might be 100-500 generations. It cannot be used, for instance, to try and prove descent from a specific ancestor, only that ancestor's lineage, if known. For instance, if you are an East African with a Y chromosome with all the characteristic Y-DNA mutations common to most Arabs, then it is a general certainty that your lineage has Arabian origin, but this does not prove for instance that your lineage descends from say, Aqeel ibn Abu Talib, just that you and Aqeel ibn Abu Talib share a common ancestor who lived thousands and thousands of years ago.