Location: Dressrosa City Area
Petitioner: Ship Carpenter Tohbo
Reward: General Store Gift, three Zoro's Cube Fragments, 74,000 Berries
Objective Reward: Feeble Ball
To unlock this Side Story you first need to complete the events of Dressrosa, culminating in the defeat of Doflamingo. Once you've done everything in Dressrosa, left for Waford, and returned in Chapter 9, a load of side content will appear in the city. You'll find the petitioner for this Side Story in N.R.P. Elevator, in the southeast of Dressrosa. He's a short walk from the elevator.
Tohbo is another carpenter of Water Seven, like Franky, and he wants to help fix up Dressrosa in the wake of Doflamingo's rampage. Alas, the materials he needs aren't to be found in Dressrosa. Franky proposes heading to Water Seven to pick up the items Tohbo needs. Hop back to the Strange Place and head for Water Seven.
Once you're in town, use Yoisa Travel to jump to Dock One. Head to Material Depot, the southern subsection of Dock One, and you'll see a series of partitioned storage spaces. Inside the first one you see when you cross the bridge into Material Depot you'll find the Tohbo of the past. Speak to him to receive Repair Lumber.
Franky's not done yet. Next, use Yoisa Travel to jump to Water Seven City Eastern Area, just outside Dock One. Head northeast to Canal Restaurant. There's a Franky Family Follower here who will let you use his manhole to enter the Sewer. Go to basement level two and you'll be a short walk away from the Franky Family's underground hideout. Proceed to the large berth where the Going Merry was being kept earlier in the game and you'll find a Franky Family Member on the lower level who will give you Durable Metal.
That's everything. Head back to Dressrosa and speak to that city's version of Tohbo. Grateful for the assistance, he'll hand over your reward.