Sony A6400 has a Sony E lens mount and currently there are 177 native lenses available for this mount.
Sony A6400 doesn't have a sensor based image stabilization system but 36 of these lenses already comes with optical image stabilization.
Since Sony A6400 has a APS-C sensor, it has a focal length multiplier of 1.5x so you have to multiply lenses original focal length with this multiplier to find the Full Frame equivalent focal length of the lens when mounted on A6400.
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Sony A6400 Lenses with Image Stabilization
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