Not Outputting

[Mekire]

Let's look from line 5.  If the conditional in line 5 evaluates to True we enter that conditional block.  Then if the conditional on line 6 evaluates to False the program ends.

What you want (presumably) is and, not a second nested if:

if (a + b) % 2 == 0 and (c + d) % 2 == 0:
    print("YES")
elif (a + b) % 2 != 0 and (c + d) % 2 != 0:
    print("YES")
else:
    print("NO")

Also it seems it could be simplified to this:

if (a + b) % 2 == (c + d) % 2:
    print("YES")
else:
    print("NO")

As both of the first two conditionals are asking if they evaluate to the same thing.