I recently replaced the focusing screen on my Canon EOS 6D. I received the new one with the mounting tab to the right in the box but the original was in the camera with the mt to the left. I mounted the new one with the mt to the right, since the instructions leaflet is not clear about that (figure D seems to show the mt to the right). I tested the camera and everything seems to be ok, focus and exposure, but I'm unsure if I did it correctly. Maybe it doesn't matter which side faces up or down?
Every Canon camera I've ever seen that has a user replaceable focusing screen has the large tab, intended as the point of contact for the custom tool Canon supplies with all replacement screens, on the right as you look through the throat of the light box. This is confirmed in this video from the Canon Professional Network.
If the focusing screen you removed had the larger tab on the left, it was almost certainly installed improperly, though I suppose it might be possible for a third party manufacturer to make one for the 6D that has the tab on the left. If the screen you removed was either of the Canon Eg-A II(pre-installed), Eg-D, or Eg-S, then the tab should have been installed to the right.
Any etching on the screen, such as gridlines or the squares indicating AF points, should be installed facing up towards the pentaprism. The textured surface on the bottom should be uniform over the entire surface of the screen. Please do not touch the textured bottom surface! It is very easy to damage
It may also be possible that the large tab on the right has been broken off at some point, leaving only a smaller tab on the left. As you can see in the image below, there is a smaller tab, circled in yellow, on the left side of the focusing screen, while the larger tab, circled in red, is mostly hidden by the tool holding the screen via the larger tab.