It has 2x2048MiB
The GTX 690 is a dual-GPU solution which means that it's two slightly crippled GTX680s glued together on the same PCB. Each GPU comes with its own memory.
When multiple GPUs are used during gameplay each GPU works independently either on the same frame (interleaved, but this is very, very old) or on alternate frames (most common).
Since sequential frames are often nearly identical to each other and usually contain the same scene elements, it stands to reason that when two GPUs are working on sequential frames independently, they will require most of the same information to render each scene. This results in the 2048MiB of GDDR5 on each GPU containing very similar data at any point in time. They will not be perfect mirrors of each other (as that would result in the two GPUs doing the exact same work, which would negate the whole point of SLI/CrossfireX) but there's a lot of overlap in that textures, models, geometry, shaders, etc... will be present in both of the 2048MiB blocks.
It is not possible for the two processors on the GTX 690 to share a combined 4096MiB of GDDR5.