If I attack a 9 Might unit twice with Kayn (6 Might), does the damage from the first combat carry over to kill the unit in the second combat?

Ruling: No, damage does not carry over between combats. Damage heals after every combat, even if nothing dies.

Sequence:

• First combat occurs between Kayn and the 9 Might unit
• Neither unit dies (Kayn deals 6 damage, opponent deals 9 damage)
• Damage heals on all survivors
• Second combat occurs with both units at full health again
• Neither unit dies again

Nuances:

• A combat can resolve without having a clear "winner" (when neither unit dies)
• The player who controls the battlefield remains in control after such combats