Can I control a Mac running 10.6.8 at one location from a mac running 10.10 at another?

I would say yes based on the information you’ve given.

However there are a few things you should be aware of first.

(A) You must have a good working knowledge of private networks (LANs) and public networks (WANs), differences between fixed and dynamically assigned IP addresses, firewalls and probably VPNs depending on how secure you want non-local remote connections to be.

(B) VNC (aka Apple Remote Desktop) is built into every Mac (it’s part of the OS) so you won’t need anything ‘extra’ such as LogMeIn or TeamViewer. Mac to Mac it should work fine as long as the requirements in (A) are met by you or someone you know.

(C) PC to Mac is also possible with, usually free, software such as TightVNC or RealVNC. Neither will work until you enable certain settings on the Mac first.

If you’ve a Mac handy, does not matter which OS version as it will be the same in all of them, explore the options in System Preferences > Sharing > Remote Management. They should start giving you an idea of how to achieve what you want. Then move onto exploring your router’s GUI and it’s Advanced Settings. Specifically the Port Forwarding section. Depending on which router you have this may not be that obvious as most, if not all, routers supplied for residential broadband users have a section usually labelled ‘Games’. This is where the port forwarding rules will be.