As the title says, there are cases within the Daggerheart rules where you use a die other than a D12 as either your hope or fear die.
Such as, “Signature Move”: Name and describe your signature combat move. Once per rest, when you perform this signature move as part of an action you’re taking, you can roll a d20 as your Hope Die. On a success, clear a Stress.
or
This feature for the Demon of Wrath:
Battle Lust - Action: Spend a Fear to boil the blood of all PCs within Far range. They use a d20 as their Fear Die until the end of the scene.