You can use DDE, which is specifically meant for communicating between apps in VB6. It can be used in .Net, but DDE is an older communication method and not really well supported in .Net.
I've done it using NDdE, but even that is no longer maintained or supported.
However, if you're willing to look into it, here's a link to download it:
http://ndde.codeplex.com/Release/ProjectReleases.aspx?ReleaseId=4828
It works pretty well, but given the lack of support, it is probably not your best option.
Since it looks like you're looking for something really simple and you don't care that it's a hack, you could always just post messages to a shared database, or write files to a pre-determined location and have the two apps look there. Web services are an option, but I doubt there is much support in VB6. (It's been years since I worked with VB6, so I don't know what kinds of 3rd party options are available for this.)