How does motorcyclists prevent their right hand wrist and left hand wrist from hurting when operating the 2008 Honda CBR600RR s?

Uper sport motorcycle?

Strengthen your wrists. Racing motorcycles are designed for riding at speed. There are not designed to be comfortable.

Good health

By adjusting their bars, small adjustments can make all the difference, if you have broad shoulders often the bars need to be turned out by a few degrees. When speed picks up to 40 or 50 the airflow will support your chest a little, taking some of the weight off your wrists. Try not to ride with your arms straight.

Over a period of time your body will adjust to this position and you will be able to ride for longer periods.
I used to have the same problem with a Honda Firestorm which got better over time. I found that town work was a pain (literally) but once zipping along at 80mph it was not a problem.
Unfortunately a woman reversed into it while parked up so that was the end of that one. I replaced it with a Fazer 1000 and can ride for miles on that with no pain.
BLISS.

Supersports have an extreme riding position that puts stress on your wrists and lower back. It doesn't bother the young guys too much, but if I'm riding a CBR 600 more than 15 or 20 min., it better be the chiropractor. 8^<

Seriously, this is one drawback of this kind of motorcycle. They're not made for general purpose riding, but a lot of guys use them for that.

Get a different motorcycle. The riding position on a "sport" bike like the CBR requires the rider to lean forward and support his/her weight on their arms/wrists. NOT the most comfortable position for most riders. A cruiser or touring style bike allows the rider to sit upright and maintain a much more comfortable riding position for long distance rides.

OUCH! I have CTS and arthritis. I can only go an hour on my old Honda 4, and that's at only 65 on I-10.

Try padded grips, change ' bar angle. Better seat, more ergonometic? Also, check motor mounts/carb sync/tune/plugs. Any of these can cause bad vibes. Also a throttle lock.

Also a quarter fairing. The wind is fierce out here. Constantly keeping your nose on your heading is very tiring.

You don't. Ride a touring bike if you want real comfort

Take short breaks often and early!

The alternate is to exceed posted speed limits and let wind loft remove weight from your forearms… Good Luck!

Get a large tank bag so that weight of chest rests on it instead of straining wrists- Old European Cafe Racer touring technique. Other wise consider a cruiser or bare bike- or handle bar risers, extra foot pegs mounted forward on engine case guards or front frame.