Photoshop CS6 probably has the most overhead per pixel of any program (i.e., is probably one of the worst for opening huge images like that).
You are not going to be able to view a 11GB image without too many problems. These images are specifically known as gigapixel images and there's actually a lot of research/development that's gone into this subject in the past few years. Image viewers/editors are not designed to operate on files of that size; 32-bit viewers in particular are very likely to exhaust their address space, and 64-bit viewers might not be much better.
The key point is that your image is not 11GB. It's 11GB compressed as a
.png file. As an uncompressed bitmap (which is what an image viewer must convert it to in order to display it), it could well be over 50GB-100GB of data depending on how well it compressed.
If you only have 12GB of RAM, you might try restarting your system (to close everything down and free up as much memory as possible) and then loading the image in a 64-bit version of Paint.NET. If that doesn't work, then you'll probably want to start looking into something like VIPS, which is specifically designed to process large multi-gigabyte images in small chunks using multiple threads. This will not allow you to directly view the image, but you can break it down into smaller chunks that you can view.
You might also look at HDView, which is designed to process and display large images in a web viewer, and the GMaps Image Cutter is designed to do the same and present it in a Google Maps-like interface (works on more browsers/platforms than HDView).