When I checked it on System, it says 8 GB RAM. But I wonder, if I put 16 GB of RAM in the two slots of my MacBook (2 8GB sticks) will it work?
Some Mac's can utilize more then the official amount stated however according to EveryMac.com, the actual maximum amount of RAM a MacBook Pro "Core i7" 2.66 GHz 17" Mid-2010 can utilize is 8 GB.
I've found that information presented by EveryMac.com to be very accurate in this area and wouldn't waste my time or money trying to put 16 GB in this model MacBook Pro unless it can be corroborated by an authoritative source.
As mentioned in the comments by RedEagle2000, "Mactracker says the same" and they too are known for being very accurate in this area as well.
Also at crucial.com, from Micron Technology and one of the top Semiconductor producing companies in the world, the model you have can only take 8 GB.
I will add I currently placed 16gb of 2x8gb sticks in my Macbook Pro 6,2 i7 2.66ghz and it worked- however in a short time it gave kernel panics and shut off and on at an alarming rate. if you are going to try this successfully- I recommend trying it with TESTED ram first- which probably isn't easily done- but I seemed to narrow it down to quality of the RAM sticks I used. I don't have funds to toss in the trash to keep trying by buying CAMXposure