What subsequent event or events were dependent on the action of the coup d'etat against Ngo Dinh Diem?
First of all, please note that his name ended with an “m,” not an “n.” You misspelled it in previous questions as well. Some teachers might be inclined to drop your grade for this.
It is not completely possible to know what might have happened if Diem had not been removed from power through this coup. We can only speculate as to which subsequent events could only happen because of the coup. One possible answer is that the terrible instability in South Vietnam’s government could not have happened if Diem had not been removed from power.
Diem was ousted and killed in early November of 1963. In the next two years, South Vietnam’s government was extremely unstable. The country went through seven changes of administration between Diem’s death and the rise of Nguyen Van Thieu in June of 1965. This instability did not help the South Vietnamese war effort. Instead, it made their government look even less legitimate and popular than it had looked under Diem.
It is at least possible to argue that the extreme instability in the South Vietnamese government would never have happened if Diem had not been overthrown in the coup of November, 1963.