Negative battery cable ground issue

I'm not positive, but I think the open hole there is the one you want. It looks like the threads are ok.

Is there a hardware store near you that would sell you an M6-1.0 bolt to try on for fit?

 

The small hole is the correct one for the Gen 2 (-) battery cable. Apparently the bolt was over torqued and snapped off.
The larger hole next to it just has a 12mm headed bolt with nothing else. Think it just clamps that brace.

A couple options right off the top of my head:

1. For me: I would use a dremel tool to cut a slot in the broken bolt and then just remove it with a flat head screwdriver. This usually works a bit better for me than drilling in an awkward spot like that, but drilling is also an option. especially if you have left twist bits.
2. The 12mm headed bolt has a head with an integral washer, so the head is wide. I would just thread in that bolt most of the way, slip the (-) cable terminal under the head as I'm tightening it the rest of the way, clamping it between the bolt head and the car body. At best, a temporary fix.
3. remove the bolt holding the chrome tie down that's next to both of those holes. Loosen the (-) post clamp to ensure you have enough cable and then slide the 'hole' end under the trunk trim so you can reinstall the chrome tie down with the bolt passing through the (-) cable terminal. Then reattach the (-) post clamp.

 

If you want to extract broken bolt,
Left Hand Drill Bit Set, 13 Pc.
Or
Screw Extractor and Left-Hand Drill Bit Combo Set, 10 Pc.

 

Option two would work, just doesn't have the full strength connection. Always possible the bolt may loosen and the connection fall apart.

 

If the bolt head broke off due to being over tightened, it will probably come out pretty easily with the first suggestion by @TMR-JWAP. IE, cut a slot in it and remove it with a screw driver.

If it broke off coming out, then you'll need some ver careful drilling and a screw extractor. Even then, iff it's really tight, you'll want to be careful that you don't snap off the screw extractor.

Since it looks so clean, I think idea #1 is probably the easiest way to do it. I've removed a lot of broken screws that way.

 

Take ONE jumper cable.
Attach one end of it to the negative battery post and the other end to a frame grounding point within 3 feet or so of the battery.......where it will clamp on solidly.
Drive it to a repair shop that you have previously contacted......where they should have the tools and expertise to fix it right in about 10 minutes. Charge: Less than $100.