What is the name of this and where or what website can can I go to buy this.... The back of the instrument cluster

 

That's the dashboard instrument cluster. If you find one, you will probably find the whole unit, complete with the gauges and plastic lens on the other side of it. It's a set of precision instruments and not considered user serviceable as far as disassembling it, although I'm sure people have done it.

Check eBay or other parts source for one that is close to the mileage on your odometer so you don't have to report a +/- mileage difference on your vehicle title or ride around looking at 300,000 miles on a vehicle that you know has half that on it. Those units are also very car specific. Don't rely on appearance. Make sure to get the right replacement or it won't function properly and could cause bigger problems.

By the way, thanks for the good photo. That burned spot on the board is where the solder fails on a lot of the 4th Gen clusters and short circuits certain things on the cluster. That spot is responsible for the infamous "brake lamp warning" and other stuff. On my cluster, which needs replacing too, it left the brake lamp indicator on so long that the bulb burned out. Then it killed the temperature gauge, which now sits at dead cold, all the time. I actually smelled the wafer board burn when it went bad.

Luckily it has not spread to any other gauges or lamps. Still have speedo, odo, CEL, etc. I don't like riding without temperature engine temperature monitoring, but I have to do that until I get some free time to tear the cluster out and replace it. It might not ever get replaced as long as the other stuff keeps working. I know when/if my Honda is running hot.

 

I actually found one but I guess I'm going to have to report difference. I have looked near and far and I kicked out at the salvage yard. Buying it from Honda was $500 original but I was getting a discount around $350 but they don't sell them anymore