per reply#6 https://forums.adobe.com/thread/2089792 Education version of CS6 is no longer available, so you will have to pay the full price
Link to buy CS6 via telephone http://www.adobe.com/products/cs6.html read all the way to the bottom
According to what I read in a forum message, Mac newer than 10.7 must subscribe to the Cloud instead of buying CS6... and someone with Win10 must also subscribe to the Cloud since CS6 is not compatible (meaning the sales person will ask your operating system and will not sell you CS6 if it won't run on your computer... I don't know if that means only Win7 and you may not buy if you have Win8)
Please report back with your operating system if you are able to buy CS6
As far as I am aware you can upgrade your LR4 to LR6. However you will have to check your OS to see if will meet the specs for LR6, I think Win 8 or Mac OSX 10.9 or higher and 64 bit. You can download the trial of Lightroom CC 2015 to try and then license it with the license key before the trial 30 days runs out.
That gives you time to do your checks and ensure it works before paying.