I'm an amateur musician that make live performances in friends confraternization parties and bars. I have a Yamaha's MG206C-USB Analog Mixer that is able to transfer digital sound in 20 independent channels to a computer through an USB port using ASIO drivers provided by Yamaha, so that it would be possible to produce it in the software supplied with the equipment and generate a stereo, or sorround, mastered music.
Is SONAR X3 Studio Suite able to receive the signal directly from this mixer? The mixer is supplied with the software CUBASE AI 6 and, to have all resources I need, I would have to update to Cubase 7.5 but because of the conditions and limitations of the software supplier for activation of the program, it is boring me. It's importante to inform that I live in Brazil. Will I be able to activate SONAR X3 Studio here in my country?.

Yes Cakewalk is an international company and over the internet everyone is equal. As long as you have a credit card or Pay Pal account. 
You can download it once you open an account. It cost nothing to sign up. 
Sonar should recognize the Yamaha if it uses ASIO drivers. 
It would be good if someone here at the Forum owns that mixer and can say "yes it works"

As Cactus indicates, any interface using ASIO drivers should be compatible with SONAR, and I have seen a few posts by members using Yamaha MG-series mixers without issue.
 
I am not aware of any registration/activation issues or limitations with SONAR in other countries. Activation is by entering a registration key e-mailed and/or downloaded from your Cakewalk Store account along with the software after purchasing online.

Cubase AI4 offers direct digital connectivity to the stereo buses of MG "USB" models for audio recording and editing. 
 
Yamaha is not saying much but it looks like this mixer is only the typical Stereo in/out that mixers in this price range offer. So this is not a 20 channel interface. The info is a little misleading and even at a few music retail sites they seem to fail to mention this. It only says' USB connection. 
 
Cubase / Stienberg's registration is enough to send you looking somewhere else for software It took me a week to activate Wave Lab into another computer. You have to wait for them to send a totally new activation code. You need to install the E key or what ever software. I think I spent over an hour dealing with this.. And every time you want to post on Stienbergs user forum you need to go through 4 pages of cr-p first. no wonder they have a dead community. You can't even post questions on software sub categories you do not have registered with them. I gave up and now use Gear slutz if I have a question. 
 
This is why I use Sonar.. I think they have the best open door registration policy and customer support. 
Sonars user forum is one of the most active and helpful of any I belong to. 
 
Sonar X3 Studio is a wise choice. best bang for the buck of the 3 versions.