update software ios 6 cannot work and my iphone 3 gs have not menu "software update

You won't have the option to update wirelessly unless you are running iOS 5 or higher. If you aren't, your only option is to update using iTunes (see "Updating your device using iTunes" here: http://support.apple.com/kb/HT4623).

If your computer is not connected to the internet you can't update your phone. (It doesn't matter if you can sync your phone or not.) You will have to connect your computer to the internet first, then update your phone using iTunes.

What it is telling you is that your computer is not connected to the Internet. You need an internet connection to download the new iOS software and to complete the activation of the phone after it has downloaded and installed.