Give an example of the input to receive an output "NO".
EXPLAIN YOUR CALCULATIONS!

a = int(input("enter a "))
b = int(input("enter b "))

if((a+b)%3==0 and b//a != 2):
        print("YES")
else:
        print("NO")

Solution
(a+b)%3==0 and b//a != 2 needs to be False to get printed NO

since we have operator and its enough that one part is False

a=4
b=3
(3+4)=7
7%3 = 1 == 0 False

Give an example of the input to receive an output "YES". 
EXPLAIN YOUR CALCULATIONS! 

a = int(input("enter a "))
b = int(input("enter b "))

if((a+b)%3==0 or b//a == 2):
	print("YES")
else:
	print("NO")

In order to get YES
(a+b)%3==0 or b//a == 2  must be True

since we have operator or its enough that one portion is True
(a+b)%3==0 if this will be True that will be sufficient to get YES

a=3
b=6
(3+6)=9%3=0 ==0 True