Hooves of the Shadowbeast

Whenever a card with 6 or more

is put into your banished zone, you may destroy this. If you do, gain 1 action point.

Battleworn

Rulings

From the Monarch release notes

You choose if you want to use Hooves of the Shadowbeast’s ability at the time a card with 6 or more is put into your banished zone.
You can only gain action points during your action phase. (You can still use this effect during your opponent’s turn, however you would not gain the action point.

Keyword notes

Battleworn - Equipment that wear down after each time they are used to defend. If you defend with a card with Battleworn, put a -1{d} counter on it when the combat chain closes.

When you defend with a card it remains on the combat chain until the chain closes, therefore you cannot defend with an equipment multiple times on the same combat chain.
A -1 counter stays on the card until the card is destroyed or the game ends.
If the defense of a card that is defending is below zero, its defense value is considered to be zero.
When this card is destroyed, it is sent to your graveyard. (Not when it has 0)
When this card is destroyed, it is sent to your graveyard.
If the defense of a card that is defending is below zero, calculate as if its defense is zero.