You seem to be thinking that the question is about the number that is equal to 452x100+10x+y, but as written I think it's about the number 452 times x times y. Please clarify which it is! If the former, then you are correct: 45240 is divisible by 60, so x+y = 4. But I'm thinking they want the latter.
The solution hinges on whether you consider the number 0 to be "completely divisible" by 60. When you divide 0 by 60 it leaves no remainder, so I think xy=0 is a possible solution. Suppose x = 0, then y can be any value imaginable, and thus x+y can be anything, and so all choices given are possible.
But i would guess that your teacher isn't expecting a solution based on xy = 0, or else there would be an "all the the above" choice. So let's try another approach. Since 452 = 4 x 113, then since 452xy is divisible by 60 this means (4 x 113)xy is divisible by 60. Since 113 is prime, it has no common factors with 60. Thus 4xy must be divisible by 60. Divide through by 4: xy must be divisible by 15. Thus xy=15N, where N is some integer. We've already seen what happens if N=0, so let's try N=1: this means xy equals 15, so xy must be either 1 x 15 or 3 x 5, which means the sum is either 16 or 8. Thus the first answer choice (8) is a possibility. If N=2 then xy = 30 and x+y could be 1+30=31 or 2+15=17 or 3+10=13 or 5+6 = 11. None of these are given as choices. It's pretty easy to show that for greater values of N the sum x+y will always be greater than 11, so none of the other given choices are possible. I would therefore say that of the choices given x+y=8 is the answer they're looking for.
