I ran SiSoftware's Sandra which gave me the following data:
How can I interpret if this computer (HP Pavilion dv6-6b50ep Entertainment Notebook PC) supports SATA 3?
If the values displayed are true, then yes.
G3 is probably generation 3 abbreviated. SATA600 stands for the the 600MB/s peak throughput of SATA 3.
I'm skeptical about the "up to" part, but other than that, it should support SATA 3.