1. Preheat the oven to 400 degrees F. In a medium saucepan, bring water to a boil over high heat. Add potatoes and carrots and cook until both can just be pierced with a knife and water has just returned to a boil, about 3 minutes. Drain, run under cold water and drain again.
2. In a medium bowl, toss together potatoes and carrots, 1 tablespoon oil, 1 teaspoon garlic, 1/2 teaspoon salt and 1/4 teaspoon pepper. In a separate bowl, combine scallops, lemon zest, dill, capers and remaining oil, garlic, salt and pepper.
3. Divide potatoes and carrots among four 12-by-15-inch rectangles of parchment paper or aluminum foil. Top each with 1/4 of the scallops. Fold parchment or foil over scallops to make packets. Place packets on two rimmed baking sheets and bake on separate racks until scallops are just cooked through, 10 to 14 minutes.