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1 d 4 means one four sided die, so you'll get a random result 1-4
1 d 6 means one six sided die, so you'll get a random result 1-6
so a weapon that does 1d6 damage will tend to do more damage on average than a weapon that does 1d4 damage.
1 d6 is a six sided die. So 1-6 damage.
So 1d6 is the better weapon as it has a higher damage potential
D&D (the system the game is based on) uses different sizes of die to differentiate damage etc., for example a dagger usually does 1d4 (so numbers from 1-4) damage, while a greataxe does 1d12 (so 1-12 damage).
If you have higher number in the front, that means rolling that number of the same dice - 2d6 is rolling 2 six-sided dice with the outcome being from 2 to 12.
Yes you are rolling 2 6 sided die, giving you a 2-12 damage range.