Answer:
Discrete variables are those whose distribution will only take a finite number of values which are represented by integer values only. 
Continous variables on the other hand could have an infinite number of points inbetween two integer values. With the values inbetween being decimals. 
Step-by-step explanation:
a. The number of textbook authors now sitting at a computer :
A discrete random variable 
Number of authors will be an integer value. 
b. The height of a randomly selected giraffe ;
Continous random variable 
Possible height value : h > 0
c. The responce to the survey question "Did you smoke in the last week" 
It is not a random Variable 
The response isn't numeric 
d. The amount of rain in City B during April 
It is a continous random variable 
Possible values ; amount of rain > 0
e. The time it takes to fly from City A to City B
It is a continous random variable 
Time could take up seconds value ;
Possible values : t > 0
f. The number of light bulbs that burn out in the text week in a room with 17 bulbs 
It is a discrete random variable 
Number of bulbs is defined