wooooah there, ok you WONT need 12 shots....for your lower teeth each 8 is innervated by a nerve, which is anaesthatised by a regional block, the ID block, you may also need a long buccal nerve injection so thats another 2.
Then theres the uppers, you'll need an injection from the outside aspect of the tooth (buccaly) and also palataly. This won't hurt as much as it would if it were done at the front of the mouth, due to the mucosa being thicker here, so it won't distend as much. Also don't worry about seeing eight needles lined up, it's the same needle and a measured amount of anaestheic is injected at each site.
Four at once IS alot, but thats not saying it can't be done, the only thing is you may have swelling and brusing in ALL areas of your mouth. And forget eating (though i doubt you'd want to!) as you'd probably chew your cheeks and tongue without feeling them.
Chelle is right about a condition called dry socket, this is breakdown of the clot which forms after extraction. This is extremely painful, but easily treated. Factors likely to predispose you to it are smoking, alcohol, dry mouth due to drugs, and not following post op instructions properly.
I doubt in your case Brandon they will need to cut your jaw, as your teeth are not impacted (ie growing the wrong way) The only other case scenario where they would need to cut it is if you have misshapen roots, although without looking at the radiograph i can't tell you that. It really isn't that big a proceedure, only tiny amounts of bone is cut away, through an insicion made in the gum flap.
This can be done under LA. Personally from what i have read i'd say do it under sedation, it comes across that you are quite anxious about it, and with 4 teeth it may be too much for you.
I extracted 2 upper canines on an EXTREMELY nervous patient 2 days ago under LA. The lady was so nervous she was physically shaking. She didn't however push me away, that meant i got both teeth out in less than 5 minutes. She was so happy and relieved she started crying and wouldn't stop hugging me!!! Apparently the teeth had been causing severe pain for a long time, but she was simply too scared to get them out and had countless sleepless nights and days off work.
Afterwards she said she couldn't believe she'd worried so much over a simple thing.
Dentistry HAS changed alot over the years, pain control has never been better. Unfortunately the negative attitude still remains, and thats something we have to battle through on a daily basis.
Wow sorry for the long reply, hope it helps