32 BIT is so easy to install

Open the Terminal
Download the file from here using the wget command:
The name of the file is AdobeAIRInstaller.bin
Save the file in the Home folder (Places > Home Folder)
Run this command:
chmod +x AdobeAIRInstaller.bin
Now run this command:
sudo ./AdobeAIRInstaller.bin
The normal installer will open, install it. From now whenever you download a .air file, just double click it and it will be installed.