Shifting level voltage of a signal
Does someone has a simple idea of how to do it?


Simple is usually best.


  High level is 12 and low level is 0V.


Subtract 6 volts DC from the signal using an op-amp circuit. There are plenty of examples on the internet - go google op-amp mixers.


  About source voltage, I just have positive ones, of 12 and 5 volts.


You need to generate a negative supply voltage and, again, there are plenty of examples on the internet. Google inverting buck regulator or inverting charge pump or isolating DC/DC converters.