Go orange. I like orange!

Pink is whimpy. Blue is sort of sad. Green is sort of corny. Black is really evil.
Orange!!!
Now, it usually helps when you tell us WHAT soundcard you have.
I will assume that is some type of Sound Blaster type of thing. The colors are there to more easily tell what each jack does. I am assuming that one is for the Line Input, one for the Mic Input, one for the Speaker Output, and possibly one for Headphone Output or possibly some sort of digital output. Who knows? You didn't tell us anything except that the Green is the Mic Input.
So, you have a mic input and a line input. They are used for two different things. The mic input is used to plug a mic directly into the soundcard. It has a "microphone preamp" on that jack. Microphones need amplification.
You have a Line Input. This input is used to interface components that output a Line Level Signal, such as home stereo components, and..............MICROPHONE PREAMP'S!!! Cool!
Now, your mixer is a Line Level device, meaning it outputs a line level signal. It SHOULDN'T be plugged into a Mic Input, because a line level device is MUCH louder in output than a microphone is. Thus, the line level device, like a mixer doesn't need to be amplified. By plugging your mixer into the mic input, you probably can't turn the mixer up very loud before you get a very distorted sound. Now if you were to plug your mixer into the Line Level Input of the soundcard, things will start to sound much nicer.
If you have a mic preamp box, such as maybe a ART MP, or a Joe Meeks something of another (who can keep track of all the different models of low end preamps they put out?

) that would also plug into the Line Input on the soundcard. Obviously if you want to switch between the mixer and the stand alone mic preamp, you will need to either change the connection at the soundcard for the device you want to use, or connect everything to a patch bay and make the connections there.
Hope this helps.
Ed