Let's start by narrowing it down to make it simpler:
Kevin is 6 years younger than Katie
Melanie is twice as old as Kevin.
So, to start off with, Melanie is twice as old as Kevin. That would make Melanie 12 years old, and Kevin 6 years old. I'm not too sure about Katie, however. But this is what I got:
Kevin: 6 years old
Melanie: 12 years old
Katie: ?
Hopefully that helped a little! :)