Change your file permissions… Like this
First check who owns the directory
ls -la /usr/local/lib/node_modules
it is denying access because the node_module folder is owned by root
drwxr-xr-x 3 root wheel 102 Jun 24 23:24 node_modules
so this needs to be changed by changing root to your user but first run command below to check your current user How do I get the name of the active user via the command line in OS X?
id -un
OR whoami
Then change owner
sudo chown -R [owner]:[owner] /usr/local/lib/node_modules
OR
sudo chown -R ownerName: /usr/local/lib/node_modules
OR
sudo chown -R $USER /usr/local/lib/node_modules