Nikon D6 has a Nikon F lens mount and currently there are 316 native lenses available for this mount.
The latest released lenses that are compatible with the D6 are the Nikon Micro-60mm f2.8D, the Carl Zeiss Makro-Planar T2/50 and the Nikon 28-70mm f2.8 ED-IF.
Nikon D6 doesn't have a sensor based image stabilization system but 71 of these lenses already comes with optical image stabilization.
Since Nikon D6 has a Full frame sensor, it has a focal length multiplier of 1x so lenses will provide their original focal length on D6.
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Nikon D6 Lenses with Image Stabilization
Nikon D6 Lenses with Weather Sealings