Any language can be used to create server-side processing. It's just not going to be CGI as you know it. Standard CGI can be written in any language you've got an interpreter for and writes output to STDOUT. Other than that for languages like VB or assembly or whatever, you need to make a DOS-like program which can read from STDIN (only necessary for POST requests) and write output to STDOUT. The rest of the input can be found in environment variables.
So in short it works like this:
1) Client enters URL: http://server.com/cgi-bin/vbprog.exe
2) Webserver sets the proper environment variables, and executes vbprog.exe
3) vbprog.exe processes the environment variables and writes HTML to STDOUT and terminates.
4) Webserver sends HTML to client
Since STDOUT is typically a DOS thing, it'll be a lot easier to write it in VB.NET rather than VB 6.0. And since I've never done this before, I can't give you more technical details on how to do it.
It is also possible that your teacher is thinking of a different technique that I'm unfamiliar with.