Solution:(a) (a) I will be assigning a new project to my manager. (Correct)(b) My manager is assigning me a new project. (The meaning of the sentence has changed)
(c) My manager has assigned me a new project. (The meaning of the sentence has changed)
(d) I am being assigned a new project by my manager. (The meaning of the sentence has changed)
Note (The meaning of the given sentence is - My manager will be assigned a new project by me.