Could someone please explain how the 10 dexterity under the hit/dc works. Does it mean that if the enemy's dc is above 10 it doesn't affect it?
The "10" listed there is the roll the target has to beat in order to take half damage instead of full. The Dragonborn's Breath Weapon is an AoE effect that forces targets to make a Dex Check. The character sheet has calculated that the DC of your character's Breath Weapon attack is 10. So, all targets make a Dex Save to try and beat a 10. They get to add their Dex mod to the roll, and if they are proficient in Dex Saves, their Proficiency Mod.
So if the target is not Proficient, but has a Dex mod of +3, they need to roll a 7 or more to pass the Dex Check caused by your Breath Weapon attack (rolled a 7, add 3 from Dex to get 10, which is equal to the DC of 10, so a pass). If they pass, they take half of whatever was rolled for the Breath Weapon's damage. If they failed, they take the full amount. Note there are a few Classes and Feats that will change that, making it full evasion on a pass and half damage on a failure.
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Could someone please explain how the 10 dexterity under the hit/dc works. Does it mean that if the enemy's dc is above 10 it doesn't affect it?
The "10" listed there is the roll the target has to beat in order to take half damage instead of full. The Dragonborn's Breath Weapon is an AoE effect that forces targets to make a Dex Check. The character sheet has calculated that the DC of your character's Breath Weapon attack is 10. So, all targets make a Dex Save to try and beat a 10. They get to add their Dex mod to the roll, and if they are proficient in Dex Saves, their Proficiency Mod.
So if the target is not Proficient, but has a Dex mod of +3, they need to roll a 7 or more to pass the Dex Check caused by your Breath Weapon attack (rolled a 7, add 3 from Dex to get 10, which is equal to the DC of 10, so a pass). If they pass, they take half of whatever was rolled for the Breath Weapon's damage. If they failed, they take the full amount. Note there are a few Classes and Feats that will change that, making it full evasion on a pass and half damage on a failure.