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The size of the wire is stated by its gauge under American Wire Gauge. Six gauge wire is size 6 AWG.
Wire gauges are defined in such a way that the lower the gauge, the thicker the wire. So, 8 gauge wire is thicker than 10 gauge wire.
Yes, the smaller gauge number, the larger the wire is.
Yes, you splice a small length of 16 gauge wire to 18 gauge wire for a repair.
The larger the wire gauge, the smaller the diameter. 12 gauge is bigger than 14 gauge.