A die is rolled four times. What is the probability that the sum of the four numbers equals 13?

I approached with x1+x2+x3+x4=13 and 1 xi bigger 1 and less than 6,

I think the answer would be 9H4 = (12C3) /6^4

But the answer is [12C3 -4 (5C2 + 4C2+ 3C2 +1)]/ 6^4

Could you explain it? (no generating function method)