Total power used is 12 watts which roughly equates to 1 amp current draw. Add 50% margin and you are looking for a wire that is rated for 1.5 amps
 
Wire is not rated in amps, it's rated by size or gauge called AWG

24 LEDs X .5 watts= 12 watts.

P (watts or power) = I (current in amps) X V (volts) THEREFORE I = P/V = 12/12= 1 amp.

For a distance of 10 feet, 12 or 10 guage wire should be enough, don't forget to install a fuse at the power source.

Take a look here for a good explanation on choosing wire gauges.

How to determine the best wire gauge
 
Kwakerman beat me to it as I was giving you formulas :D

It's good for you to become a bit familiar with the basics of 12 electric principles.

Forgot to add, that as the numerical value goes down, the thickness and current handling of the wire goes up.

So for example, a 10 gauge wire, is thicker and will carry more current than say a 12 or 14 gauge wire.
 

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