I'd check out PS Exec from Sysinternals. It does exactly what you want and does not require any VB6 goo, such as DCOM.
Getting the exe to run on machine B would be easy. Presumably you want it to run on machine A. I've never tried it myself, but this sounds like a job for DCOM.
Here's a Microsoft article that walks you through DCOM with VB6. You create an ActiveX exe on machine A, and then VB6 code running on machine B can call into the exe running on machine A. You haven't said what the exe actually needs to do, but presumably you can create one or more methods in a class to do it - whatever it is - and you can pass any necessary information between the machines with the method calls.
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