The Nginx error “[emerg] mkdir() “/var/cache/nginx/client_temp” failed (13: Permission denied)” is caused by nginx process doesn’t have permission to access this file /var/cache/nginx/client_temp, the solution is change the file ownership and group belongs to the nginx process. If you run the nginx process as nginx and group is nginx then run this :
$ sudo chown -R nginx.nginx /var/cache/nginx/client_temp
or if as nobody and nogroup :
$ sudo chown -R nobody.nogroup /var/cache/nginx/client_temp
Hope this help someone!