I am not sure the size of a 6 mm wire but on the insulation of the wire it will read awg # 14 or awg #12. If the wire was made in America it is sized by awg or American Wire Guage and that would tell you the capacity. #14 wire can handle 15 amps and #12 wire will handle 20 amps. or just over 2000 watts. If it is a lower number it will carry more current.
The wire will also have letters on it like THW or THHN. and it will read 600 volts. That is the insulation rating. If it does not read that, it is telephone wire and you can not use it.
Any minimum wire in any house in the US will handle 1200 watts, if that is the only thing on the circuit. (and if the home was legally wired)
(electrician 40 years)