The front left has 6 studs and two holes that look like the lug nuts were overtightened and broke the studs off
I corrected your statement a bit.
The nitwit drilling portion is a secondary issue.
You might want to take a close-up picture and start a new thread on this.
I’m not that familiar with backhoes (large equipment) but have replaced my share of lug studs on many brands of autos/pickups.
Most auto/pickup lug studs look like:
Which are pressed into the hub.
I’ve seen a few where the stud is screwed into the hub (but not many).
The big portion of job is to get vehicle jacked off the ground, the tire removed, and brake drum (or rotor) removed. If the back side of stud is round, then it presses in. If it has a hex end, then it should unscrew (see above pictures).
If your stud(s) are broken flush with hub or close to it. That said, you should be able to get by without using the official stud remover.
For press in studs, the first part is to get a BFH (aka: A big hammer). A three pounder works well. A nail hammer will not cut it. It also helps to get a punch smaller than the stud and hammer the stub out, as shown.
They make an official tool to extract stripped out or studs that are
not broken flush.
The second best (or first best, according to some) is to use a press to press those studs in and out:
Not everyone has access to a press, though. It also requires more disassembly and reassembly (as well as the next option).
This is an arbor press, which can work well, as well:
The third best method (which requires more work, as above) is to use a big vice (the small to mid-size ones won’t do much.
No matter which method you use, you will need to remove the brake drum (or rotor) to extract the broken parts.
To reinstall the stud – most would use the same took you used to extract the broken part out – except for the hammer/punch method.
This method works in many cases – but I recommend taking your new stud to a hardware store to get a sacrificial nut and washer for most likely both will be ruined getting a new stud in. Even passenger cars will tear up the nut and outermost washer. In some cases, it can even break the new stud.
It is possible, you might have to extract a good stud to find a replacement stud with.
Getting off subject, if a lug stud looks questionable, I always replace ‘em. I’m in the process to overhaul four different differentials shortly and part of that will be replacing the studs on all eight axle shafts while axles are out (40 studs). A lot easier job to do when axles are removed from car.
BudW