Answer:
The correct number of servings = 6.
By saying there were  servings of soup, Hector must have intended to say that there were
 servings of soup, Hector must have intended to say that there were  quarts of soup for serving.
 quarts of soup for serving.
Step-by-step explanation:
Given:
Total quarts of soup made by students = 
Fraction of the soup served to  friends = 
Each serving =  quarts
 quarts
Hector incorrectly says that that there were  servings of soup.
 servings of soup.
To find the correct number of servings and to identify Hector's mistake.
Solution:
Total quarts of soup made = 
Fraction of total quarts served = 
Thus, total quarts of soup served = 
⇒ 
Thus, total quarts of soup for serving  = or
 or 
Each serving  =  quarts
 quarts
Total number of servings can be given as:
⇒ 
⇒ 
To divide fractions, we take reciprocal of the divisor and replace divsion with multiplication. 
⇒  
 
⇒ 
⇒ 6  servings 
Thus, the correct number of servings = 6.
By saying there were  servings of soup, Hector must have intended to say that there were
 servings of soup, Hector must have intended to say that there were  quarts of soup for serving.
 quarts of soup for serving.