After starting the "checklist quest", Living on the Edge, you'll have to talk to the Mariner to start this quest. Head to the Eagle’s Cove Tannery to the western side of the island. (Refer to the location’s page for more information about the points of interest you can find there)
Inside the tannery, there are two ghouls in the first room behind an Advanced locked door. You can pick the lock yourself but alternatively, you can get the key from a bloated glowing one in the tannery’s small basement area. The power tools the Mariner is looking for is also located in the basement, inside a duffle bag. Beside the duffle bag, you can also find a red industrial trunk.
The tannery key can be used to open the locked office room in the ground floor and the safe inside. It can also unlock the alternate exit through the basement. As you exit the building, Machete Mike will come running to you and offer to buy the tools for 2000 caps. You can ask for more caps through speech checks or outright refuse the offer/ sell the tools. If you decide to keep your word, travel to Far Harbor and hand over the tools to the Mariner to complete the quest.