You receive this quest from the Addanc Dripina in the River of the Addancs.
You will need the Addanc Sight Ability to be able to see and talk to her.
To get the Addanc Sight Ability, refer to the Build a Bridge quest.
In exchange for a protection potion for Gamog, which is for the Persuade Dripina quest, Dripina asks you to go back to Gamog and ask him to send someone powerful enough to blow up the dam that holds the Addancs prisoner.
Go to Gamog, who is in the Realm of Gamog.
He says he will send Gap Tooth to blow up the dam.
Go back to the River of the Addancs and talk to Gap Tooth, who is in the Northern part.
He will ask you to bring him 30 Bannock buns, then he'll blow up the dam.
You will receive the Bring Bannock Buns quest.
When that quest is complete, talk to Dripina.
The Blow up the Dam quest will be solved.
You will receive a Addanc Bow, a Giant Protection potion for Gamog, and an increase in fame.