Since your version of Photoshop is way old and cannot use the newer ACR plug-in needed to read your new camera's CR2 files, you need to edit the settings in LR so that LR sends something other than the CR2 file to Photoshop.
Menu > edit > preferences > external editing
Using the current DNG converter and importing the DNG files into Lightroom would also solve the problem.
Subscribing to the "photographer bundle" of LR + PS to get the current version of Photoshop would also solve the problem.
Since you have purchased Lightroom 6, you can install all the updates which go all the way to Lightroom 6.10.1. However, since you are using Photoshop CS6, the latest version of Camera Raw you can use is 9.1.1. But that really isn't going to be a problem as long as you make the right choices in Lightroom. Just do as much editing is possible using Lightroom. Then choose the option when going to Photoshop to edit a copy with Lightroom adjustments. That will create a copy that includes everything you have done in Lightroom, and you can finish your work using using Photoshop. You don't have to worry about Camera Raw. You get to take advantage of all the latest Camera Raw technology built into Lightroom, and finish up what you need to using Photoshop. The only thing Camera Raw is used for is in the process of handing off the raw file from Lightroom to Photoshop. When the two programs are in sync, Camera Raw is used to convert the program to a pixel-based image as it moves to Photoshop. By choosing to let Lightroom do that Camera Raw isn't even needed anymore so you don't have to worry about it.