Hello, yes, this is difficult isn't it because of the year! What I want to say is either: He started writing a book in 1988, but I don't know if he finished it. or He began writing a book in 1988, but I don't know if he finished it. or He started to write a book in 1988, but I don't know if he finished it. I don't know what type of exercise you are doing, if none of the suggestions are suitable, then use the past simple: He wrote a book in 1988, but I don't know if he finished it. By using the past simple here we are saying that we know he began to write a book, and as the past simple is usually used for completed actions, he may have finished the book, we just don't know for sure. I hope this helps, best wishes, Annie

He wrote a book in 1988 but I don't know if he ever finished it.