I have a intranet website shared on my local network which displays tables from a sql database. I want to expand this to certain people who are not on my local network. Is it to use Hamachi to enable them to connect to my website? If not what is another way to make this possible?
Basicaly yes. As soon as your Hamachi did create a working VPN they should be able to access your local webserver.
Or open/configure your firewall/router to redirect a special external port to your web server port (which would be the easiest to use, because no external configuration is necessary).