Simple voltage drop needed

Hi rolijen, you have discussed only on the voltage rating here but have completly ignored the current rating. So before the take the following idea make sure you new 6V bulb has a current rating that is within the limit of our main circuit board.

That being said the best and safe way for you is to use a voltage regulator IC like 7806 which will convert the 12V dc to 6V DC. Do not use a zener of resistor method to drop voltage since they might burn easily if you current rating is more. You can refer to the following link for more detials

https://components101.com/7805-voltage-regulator-ic-pinout-datasheet

This particular IC regulates 5V you just have to use 7806 in place of 7805 to get 6V 

Voltage drop is the decrease of electrical potential along the path of a current flowing in an electrical circuit. Voltage drops in the internal resistance of the source, across conductors, across contacts, and across connectors are undesirable because some of the energy supplied is dissipated. The voltage drop across the electrical load is proportional to the power available to be converted in that load to some other useful form of energy.
For example, an electric space heater may have a resistance of ten ohms, and the wires that supply it may have a resistance of 0.2 ohms, about 2% of the total circuit resistance. This means that approximately 2% of the supplied voltage is lost in the wire itself. An excessive voltage drop may result in the unsatisfactory performance of a space heater and overheating of the wires and connections.
National and local electrical codes may set guidelines for the maximum voltage drop allowed in electrical wiring to ensure efficiency of distribution and proper operation of electrical equipment. The maximum permitted voltage drop varies from one country to another.In electronic design and power transmission, various techniques are employed to compensate for the effect of voltage drop on long circuits or where voltage levels must be accurately maintained.