If I had to take a guess it is a kindle fire hd 7 2012 model, and BTW there are 4 code names outside of the stuff that came out this year, they are otter, otter2, Tate, and jem. The 7" HD is a Tate model. I'm only basing this on the fact it was labeled at 7" model, but you can see the front facing camera in the pic that the 2013 models don't have. The HD model's cyanogen mod aren't listed on their website because they aren't official yet, you have to learn the process for flashing ROMs on kindles here because it's not as straight forward as some devices like the first gen kindle, and the ROMs are also posted here at xda in the development section.

Sent from my Amazon Kindle Fire HD running CM10.1 Tablet UI using xda-developers app
My Wallpaper Fix for KF2, KFHD 7", and KFHD 8.9" is HERE
Please Read the instructions and use the debugger if you run into errors.
My own modified adb drivers for just about all kindles (includes old twrp and cm versions) HERE
Tablet UI Patch for latest CM10.1 build HERE!

Please send complaints to /dev/null