need asus cpu fan replacement

My neighbor's desktop computer ASUS Essentio Model CM6850 needs a cpu
fan, it's making a lot of noise and not spinning up to speed, sounds
like a bad bearing, the fan is model AUB0812VH.

How can I look up the part number for that exact item so I can replace
the fan with a replacement the software will be able to monitor?

I took a chance and bought a same model fan but with a brown instead of
red wire (originals are blue black red yellow) and the machine wouldn't
boot - it didn't detect the fan. Thank God I didn't blow the m/b.

Any suggestions would be appreciated.