“You don't have write permissions for the /Library/Ruby/Gems/2.0.0 directory.”
The above error means exactly that, you don't have permission to write there. That is a version of Ruby installed by the Apple, for their own use. While it is OK to make the minor modifications to that if you really know what you are doing, as you are not sure about a permissions problem, I would say it is not the good idea to continue with that track.
Instead, I will strongly suggest you to look into it by using either rbenv or RVM to manage the separate Ruby, installed into the sandbox in the home directory, that you can modify/fold/spindle/change without ever worrying about the messing up a system Ruby.
Between the two, I use the rbenv, though I used a RVM a lot in a past. rbenv takes the more "hands-off" approach to managing the Ruby installation. RVM has the lot of features and is very powerful, but, as the result is more intrusive. In either case, need to READ the installation documentation for them for a couple times before starting to install whichever you want to pick.