Short Answer: 11/12
Step One
How many ways can you throw two dice?
There are 6 faces on a cube. Each cube has a different number. (Opposite sides add up to 7 -- that last fact is not important, but it is interesting).
So the total number of ways you can throw 2 dice is 6 * 6 = 36
Step Two
How many of those 36 will give you 4? To make the problem slightly easier to understand, make 1 dice red, and 1 blue and just list the ways.
Red Blue
1 3
3 1
2 2
That's Three ways that you can throw a four
Step Three
What's the probability of throwing a 4?
3 successful ways 36 total ways.
3 / 36 = 1 / 12
Step Four
What is the probability of not throwing a 4?
1 - P(4) = 1 - 1/12 = 11/12