Can I connect a Zoom G3 and a G3x together to give me the opportunity to have 12 effects available to switch in and out?
Yes, you can connect these in series, but this would be extremely sub-optimal as you'll bring in noise, and won't be able to use delays, reverb etc from the first pedal.
If you want 12 effects, get yourself a pedal that can do that, or even more.
Can I connect a Zoom G3 and a G3x together to give me the opportunity to have 12 effects available to switch in and out
Simple answer first: yes. It won't be optimal from an audio point of view as you'll be going through A/D conversion twice, but that doesn't sound like the worst problem in the world.
However - thinking of an individual G3 or G3x as '6 effects you can switch in and out' doesn't seem to me to necessarily be very helpful. These kinds of boxes have the ability to save a number of completely different chains of different effects, so even with a single G3 you can switch very easily between a number of configurations from thousands of possible combinations. For example, for one song, you could have 2 distortions pedals, a flanger, and an amp sim ... then for another song, you could flip to having 3 delays and 3 reverbs. Unless you need more than 6 effects at a time, you might have a much simpler and more fun time just using one box. If you use 2 together, they won't be able to sync the saving of their settings.
Actually I have a used G3x on the way and own a zoom B3.
You'll be able to try your idea out anyway then - for example, set up all your gain effects on the G3x, and then have that going into the B3 to provide all your ambience effects. (many of the effects, including ambience effects, on the B3 will work just fine on guitar).
If you do find that you really do need more than 6 effects at a time, then as Doktor M suggests I'd personally prefer a single box that can do more effects at once (e.g. zoom g5 can do 9, if you like the current zoom way of doing things) - though if it were me personally, I 'm running that many effects at a time, I'm probably wanting to start going crazy with some parallel routings, which I don't think these zooms can do.