...finally after some trouble and after many searches on this forum, google and others pages have managed to do it.
First I want to thank the community that gave me more ambition to do it, than make me quit to install AdobeAir.
Whole problem was the package ia32-libs(The ia32-libs package was a hack to get 32-bit packages installed on a 64-bit installation. Since Ubuntu version 11.10 (Oneiric), Multi Arch has been added. One of the objectives for it is removing the ia32-libs package)... package that Canonical has decided to end support for it.
All I had to do to install ia32-libs package was to add this repo:
1- ''deb http://archive.ubuntu.com/ubuntu/ raring main restricted universe multiversepackage source''
I followed the steps from this quick and easy tutorial:
2- then this page that leads me to this nice steps to install Adobe Air For 64-bit Systems
-----------------documentation that I used:---------------
P.S. ---as noted by Alvar, Adobe Air for Linux is no longer supported---