The answer is "it depends."
The easiest way is to find out the IP address of your machine and send your boss/coworker that URL (along with the port number). For example, if the IP address of your machine is 10.0.2.1, your Tomcat URL is:
(assuming you have Tomcat running on port 8080 per default.)
Be aware that if your machine uses DHCP to lease its IP address, your IP address may change periodically, so you'll need to look it up every time you send the link.
If you only have a few hosts on your network and no IT support and are using fixed addresses, you can edit the HOSTS file on your boss's/coworker's machine. Map myname.companyName.com to your IP address, then the following URL is valid, but ONLY on your boss's/coworker's machine:
If your company has an IT department or you're using DHCP with dynamic DNS, your best bet is making a request to your IT staffers. They can probably give you a workable solution in a short amount of time.