Does any one know about any free software for windows with which I can combine multiple videos and create a video like this?
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On Windows, for free, your best (albeit complicated) bet might be Blender.
You could create a series of several plane meshes in the layout you wanted, in front of the camera. You'd then create a separate material for each of the planes, setting them to shadeless, and giving each a different video texture. You'd have to mix the audio separately (Windows Movie Maker, or Blender also has a built in video editor).
I'll note that using a 3D approach for something like this isn't ideal at all - a 2D compositing program like Adobe After Effects would be much better (Blender itself does have a 2D compositing component, but since it uses nodes instead of layers, it might actually be more difficult).