Unless I'm missing something, the error "Could not create /Library/Python/2.7/site-packages/nltk: Permission denied" suggests that whatever command you are using to install the nltk (and you didn't say), it
is not running with administrator permissions.
So this seems like a problem with the way you administer your computer--I expect you'll have the same problem if you try to install any other non-standard python module. But if you feel that the problem is nltk-related and need to ask for more
help, please include more details, starting with your operating system (looks like OS X to me... but what version?) And please copy-paste the error messages etc. as text, not as a screen grab.
Good luck,
Alexis