The colors don't mean anything. Some manufacturer chooses some colors, others choose other colors. The color only makes it possible to know which channel is which. From one end of the cable to the other end.
If you want the right stereo channel to be sent to the right loudspeaker in your room you can be careful to connect all cables so that they do not cross. Decide that red is always the right channel, for example. The left channel can be black or white.
Or ignore the colors and let any loudspeaker be the left. Or use a test record and hear if it is right, change the loudspeaker cables if needed.
They are probably the right cables, the colors don't matter.
Install the software for the soundcard, connect the line-out output the the aux input on the amp, it can also be labeled input, auxillary input, line-in, etc..
Turn on the home stereo, start a soundfile on the computer. Open the sound mixer you got installed with the soundcard software, set the wave output active, set volume levels.