Harsh Mentor

Whenever an opponent activates an ability of an artifact, creature, or land on the battlefield, if it isn't a mana ability, this creature deals 2 damage to that player.

Duskmourn: House of Horror Commander

Whenever an opponent activates an ability of an artifact, creature, or land on the battlefield, if it isn't a mana ability, Harsh Mentor deals 2 damage to that player.

"A time may come soon when there will be need of valor without renown. Yet the deeds will not be less valiant because they are unpraised."
—Aragorn

Tales of Middle-earth Commander

Amonkhet Remastered

Amonkhet

Activated abilities contain a colon. They're generally written "[Cost]: [Effect]." Some keyword abilities (such as equip) are activated abilities and will have colons in their reminder text. An activated mana ability is one that produces mana as it resolves, not one that costs mana to activate. Notably, exerting a creature isn't an activated ability.

Harsh Mentor's ability doesn't trigger when an opponent activates an ability of a card in hand (such as cycling) or a card in a graveyard (such as embalm), even if that causes a card to be put onto the battlefield.