You could never, strictly speaking, open a VB6 project in VB.NET. Originally in VS.NET, Microsoft offered a VB6 upgrade wizard, it could be invoked from the IDE to convert snippets or, if you tried to open a VB6 project directly, it would convert the entire thing to a VB.NET project and open that. Such conversions never went completely smoothly, leaving you with some manual work to do as well as making use of classes created specifically to support converted VB6 code that should never be used otherwise. As JohnH suggested, that wizard was discontinued after VB 2008.
For a while after that, Microsoft offered a free license to a third-party tool for conversions. The free version was limited to 10,000 lines of code but, apart from that, I believe that it did a better job than Microsoft's own tool. As Herman suggested, VB6 and VB.NET are actually quite different in many ways so a straight conversion is not usually as easy as some may think.
There is still a page on MSDN that links to that tool but the vendor only mentions a free license for MSDN subscribers and even then doesn't provide a link to get it. That said, they do provide a trial version of the tool. It states that that trial version is limited to 10,000 lines of code, just as the previous free license was. I'm not sure if there are any other limitations on the trial version, e.g. expiry after 30 days, but you could always find out.
Download VBUC
That said, if you're working in VB.NET then why have you downloaded a VB6 project at all? If you're trying to accomplish something in VB.NET then the best way to do it may not resemble the way it's done in that VB6 project anyway. As we've said, VB.NET is quite different to VB6 so there's every chance that trying to follow that VB6 project is actually the worst thing you could do. Maybe you ought to explain to us what you're trying to achieve and we can give you some guidance as to how to achieve it in VB.NET and whether or not that might resemble how it would be done in VB6.