How to extend router wire?
Your question is unclear. I think you are asking about extending the DC cable from the mains power supply (probably a "wall wart" power supply) to the router.DC input jack. 

Your router will require less than 1 amp at about 12 V. Any 2-core cable of similar size will work. You need to make sure that you keep the polarity the same.

AWG is American Wire Guage. You will find metric converters online.