Answer: 1. with his family's approval 2. on a major remodeling project 3. into a bright studio
Explanation: A prepositional phrase begins with a preposition (with, on, into) and ends with a noun (approval, project, studio). Sometimes it has an article (the, a, an) or a possessive (family's) in the middle, and sometimes it has nothing but the preposition and the noun: example: at home, in time