Plywood quote question

I receive a quote today for the plywood I'll be using in my upcoming build, there were a couple terms I am not familiar with, here is what the quote looks like:

I am lucky that I can get 10x5 birch ply in my area, this will prevent me from needing to splice anything together (and the cost isn't insane compared to the 5x5), however I do not know what 4B or 4BB means. BB for plywood, to me, means B grade on both sides, however I do not know what the number before it means. Anyone know?
As far as where it says 12MM - I assume this means it's just shy of 1/2 inch and is 12MM thick. Please correct me if I am wrong.
In the email, she also said "Keep in mind the 10x5 plywood, the grain runs the other way" - I am not familiar enough to understand what this means, can anyone shed some light on it for me?
Thanks!

I am lucky that I can get 10x5 birch ply in my area, this will prevent me from needing to splice anything together (and the cost isn't insane compared to the 5x5), however I do not know what 4B or 4BB means. BB for plywood, to me, means B grade on both sides, however I do not know what the number before it means. Anyone know?
As far as where it says 12MM - I assume this means it's just shy of 1/2 inch and is 12MM thick. Please correct me if I am wrong.
In the email, she also said "Keep in mind the 10x5 plywood, the grain runs the other way" - I am not familiar enough to understand what this means, can anyone shed some light on it for me?
Thanks!