Um no, not for the cathode anyway. You need a 74hc595 output port (there are 8 on a single 74hc595) for each led of whatever color. There is nothing to stop you from having a red led on pin 1 a green led on pin 2 and a blue led on pin 3. The shift register doesn't care about colors (you may because of software issues, but the hardware doesn't) The version with a 74hc595 on the cathode is likely doing multiplexing which you are not. I'd start with the first tutorial I listed which has 8 leds on a single 74hc595 once you get that working then you can add the second 74hc595 to get the second 6 leds connected. As noted you can alternate red and green leds if you like, the hardware won't care. The software will need to know which output pin has a red and green led to tell which one it should turn on but it too doesn't care about the color only that it will turn that particular pin on or off. so if you want to end up with 12 leds (6 red, 6 green) you need 12 ports or less than 2 74hc595s Even if the red and green led are in the same package (with 3 wires coming out) the red and the green led each need one port on the 74hc595 (and a resistor between the port and the led). As to the 100nf capacitors they want while they are a good thing to have eventually you probably don't need them right now. The circuit will work fine without them, their purpose is to reduce noise and this particular application isn't switching fast enough to make that a big problem.
Peter