In Commander, if you cast your commander from the command zone for the third time, does it cost 6 more generic mana?

The Commander Tax (formally the 'commander tax') adds {2} to the casting cost of your commander for each time it has been previously cast from the command zone. The key word is previously — you count how many times it was cast before the current cast.

By the third time you cast your commander, it has been cast twice before. That means the extra cost is 2 × {2} = {4} generic mana, not {6}. Six extra mana would apply on the fourth cast (3 prior casts × {2} = {6}). This rule is defined in the Commander additional rules (CR 903.8).

So the breakdown is: 1st cast = +{0}, 2nd cast = +{2}, 3rd cast = +{4}, 4th cast = +{6}, and so on. The tax stacks each time, making later casts progressively more expensive.

Example: Your commander is Atraxa, Praetors' Voice (base cost {2}{G}{W}{B}{U} = 6 mana). Your first cast costs 6. It dies and you recast from the command zone — second cast costs 6 + 2 = 8 mana. It dies again; your third cast costs 6 + 4 = 10 mana.

This rule exists to discourage repeated commander recursion and is tracked even across zone changes, meaning the tax never resets during a game (CR 903.8).