Your request seems a little vague. Are you looking for any genre in particular? (fantasy, sci-fi, historical -and which period-). Since you want a 6mm game, I'm assuming ou want a large-scale battle game, a-la Epic
40K or Warmaster.
If you want a sci-fi game, you can try Epic
40K in any of its versions, as str00dles1 already suggested. There are many companies that make suitable proxies that you can use, or you can always check on eBay. You can also try NetEPIC (
http://www.netepic.org), which is basically an evolution of the old Space Marine / Adeptus Titanicus rules. All the rules and army lists needed to play are there, free of charge.
There's also an old but pretty good game called Dirtside II, it's a generic sci-fi 6mm miniatures game released by Ground Zero Games back in 1993. The rules are a bit old-fashioned, but they still work pretty well, and now they're available for free (along with its brother rulesets, Full Thrust, a spaceship combat game, and Stargrunt II, a platoon-level ground combat game for 15-to-28mm figures) in the publisher's website:
https://shop.groundzerogames.co.uk/. BTW, all of GZG's rules are actually generic, so you can use any setting and figures range you like, but they also include their own "official" setting, for which they also have a nice range of both 6mm and 25mm figures for their games at reasonable prices.
Now, if you want some fantasy action, look no further than Warmaster, you won't find anytyhing better than that. The rules were available for free in
GW's site for a while, but since they pulled the plug in all their old Specialist Games range now it's not there anymore. Anyway the game is pretty easy to find if you Google it. As for minis, you may wanna take a look at Kallistra (
https://www.kallistra.co.uk/) and Pendraken (
https://pendraken.co.uk/), they both have very nice 10mm fantasy figures suitable for Warmaster, and even some army pack deals on both sites.
In the historical side of the hobby, you have a plethora of figures manufacturers and rules to choose from, you'll have to be a bit more specific about the period-conflict you're interested on to give you some pointers.
Hope this helps, see you around!