Answer:
Option A is correct

Step-by-step explanation:
Let x and y be two unknown integers.
As per the statement:
"An unknown integer, multiplied by two times itself, plus two times a different unknown integer, equals negative 20."
"An unknown integer, multiplied by two times itself" translated to 
"Two times a different unknown integers" translated to 
"negative 20" means -20
then, our equation becomes:

Add 20 to both sides we have;

Therefore, the equation represents is, 