A fragile weapon breaks if you roll a natural four on the first attack in a round you make.
A fragile defensive item, such as a shield, break if you roll a natural four on the first defense roll in a round.
A “round” in this context resets at the start of your turn, regardless of where you are in some “initiative order”.
Multiattacks don’t make your item more likely to break, but, advantage and disadvantage both do.