No rule for this one
No ending or word group predicts the article of Amt. Learn it as a pair and say it out loud: das Amt.
das Amt
It's das Amt. Amt is neuter, plural die Ämter.
Ich muss zum Amt.
I have to go to the office.
No ending or word group predicts the article of Amt. Learn it as a pair and say it out loud: das Amt.