Yes you can use the OCZ Vertex 4 SATA 3 6Gb/s ssd with a motherboard that only has SATA 2 3Gb/s capabilities. SATA 3 is backward compatible with SATA 2. The international standard was designed that way. There will be a performance hit but you shouldn't notice it during ordinary everyday use. You might notice the performance difference if you are doing some sort of heavy duty complicated work.
What is the brand name and model of your motherboard? There are some really old motherboards with old controllers and old chipsets that do not work well with modern 3rd generation ssd's.
excella - Gb/s refers to gigabits. It does not refer to gigabytes. For a SATA 2 3Gb/s ssd that equates to a theoretical maximum data transmission rate between the ssd and the motherboard of about 300 megabytes per second. The actual data transmission rate will be lower for a variety of reasons.
nmwido - You'll need to go to the Biostar web page for your motherboard. Download and install the BIOS, chipset, and driver updates. There is a separate upgrade just for SATA.