Simplest way is to get the exact model of your CPU using something like CPU-Z*,
The model will be listed under 'name' as something like this:
Intel Mobile Core 2 Duo P7570
AMD A10-4600M APU
AMD Athlon 64 X2 Dual Core BE-2300
Intel Pentium E6800
Then Google to see what year that specific model was introduced. That will be the year that CPU was at it's peak compared to others. Of course, it's possible your system is using a CPU that was not top of the line even when it was introduced, or may have been sold a couple years after the CPU came out and had already been surpassed by newer processors. Still, the CPU should give you the best potential date. It's also possible if it's a laptop or very specific model to google the model number itself and if the year of introduction isn't available, you might find the owner's guide and check the copyright date.
I'm curious, why do you wish to know?
* free download, very useful utility. http://www.cpuid.com/softwares/cpu-z.html
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“For small creatures such as we the vastness is bearable only through love.”
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