The answer is a. The colon in this helps separate what he is talking about and what the project is. The other answers don't make sense because they don't have them separated like that
the answer is: I have one project for myself this summer: to research my family tree.
The correctly punctuated sentence is A: "I have one project for myself this summer: to research my family tree." This is because a colon effectively introduces the explanation of the project. The other options incorrectly use semicolons or commas in a way that doesn't effectively introduce the project.
;