***** NOT A TEACHER *****
Hello, Sherlocklelts:
May I make a respectful suggestion?
I know that you do NOT want to guess when you are taking an examination.
I suggest that you review the active and passive forms of sentences.
Then you would know that "The new handbook was finally distributed" is the passive version of something like: "The manager finally distributed the new handbook."
If the active sentence were something like: "The boss finally distributed the new handbooks," then you would choose "The new handbooks were finally distributed (by the boss)."
For "has" to be the answer, the active would have to be something like: "The manager has distributed the new handbook." That is to say, "The new handbook has been distributed (by the manager)."
When I was young, I enjoyed taking tests if I was confident that I knew the material. I am sure that you will find that to be true for you, too.