Question

An advertisement on the radio warning the public against the dangers of smoking is called a __________.
A.
public service declaration
B.
public health message
C.
public service announcement
D.
public health initiative

Answer 1

The answer is C) public service announcement

Answer 2

In school, you are taught that smoking is bad for your health.
So?
We can associate the word "danger" in the sentence with the world "smoking".

Service: Not related to health(smoking), so we can get rid of options A and B.
Health: Related to health(smoking), so keep B and D.

Message: A communication containing some sort of information. Keep B.
Initiative: As defined by dictionary.com, 
               "an introductory act or step; leading action"
               Warning the public against something does not fit, so discard D.

We are left with Option B.