US colours are
black = hot/live
Green = ground/Earth
White = Neutral
If you zoom into the photo you will see the black is connected to L or Live
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For the LEDs, it depends if the internal led has a 5v input voltage and a resistor to drop the 1.8v or if they were manufactured as 6.8 v LEDs. Most likely they are 5v with a resistor in the casing. You could sacrifice one to see or get the spec sheet for them.
Almost all pin leds I have taken apart have at least one diode that rectifies the 6.8v AC to a crude 6.8v DC. The better leds have two diodes to create a bridge rectifier
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if you use the 12v output from the supply then you will need to drop the extra voltage to 6.8v with a resistor per led
If you use the 5v you won’t need to drop the voltage but as the LEDs already have a resistor in the casing to then they won’t be as bright but that won’t be super noticeable. Most arcade power supplies like the one I show have an adjuster for the 5v so you can increase the output closer to the 6.8v you need. Caveat is that no other mod which needs closer to 5v is connected.
For the current, you will need to make sure that the 5v output supports the total current draw of the 20 leds. Most pin leds draw a tiny current in the mA range but if your 5v output from your supply has a max of 2A then you can only connect enough items that do not exceed that current output
You need to account for the total current of the pin led including the resistor. All diodes drop 0.7v across them so their current draw is fairly well know but with the resistor this will be slightly higher though again only micro or milli amps
It is very likely you can hook up far more than 20 leds to a 2A source but it’s good to know what is being used by your setup so you know how much is left
You can either check the specs for the LEDs or hook one up to PSU supply it with 6.8v Dc and measure the current with a multimeter
The power supplies are regulated so you will always get the same voltage no master the current draw up to the Max current rating
Hope that helps