For bird photography using Sony NEX6, suggset you try 70-400mm G2 lens:
http://www.sony.com.hk/zh/electronics/camera-lenses/sal70400g2. You need an A-mount to E-mount lens adapter for connecting the lens to NEX6:
http://www.sony.com.hk/zh/electr ... unt-adapters/la-ea4
I used this combination about three years ago and the quality of bird (including bird-in-flight) photos was quite okay, except that the focusing was not always sharp. I ended up using manual focusing to improve the quality.