Connecting and soldering audio cable of several earbuds, but none is working
Now that you've added a picture, the problem is clear.

The red and yellow wires that you connected actually have a second wire buried in side of them. 

That is to say that what you think is a wire is actually a two conductor cable.  

There are therefore 4 wires in all that you have to separate and solder.

Look more closely at the red wire.  If you separate the strands carefully, you should find that there is another, separately insulated wire inside of it.

The way you've soldered things together in the picture shorted the earphone outputs.  Each cable has a signal and a ground.  You've soldered the signal to the ground.

What you've done (which is wrong:)






simulate this circuit &ndash; Schematic created using CircuitLab

What you should do:







simulate this circuit