Let's calculate the probability of rolling two sixes. We can start by looking at all the pairs that can possibly be rolled:
There are thirty-six possibilities all together (notice that 36=6*6=6^2). Out of those, there is only one pair that is 6-6, so the odds of rolling 6-6 is 1/36.
Now consider the probability of rolling a number less than three followed by a number greater than two. How many ways can we do this? For the first number, we can roll a one or a two. For each of these two choices, we can roll either a 3, 4, 5, or 6:
So there are eight ways that we can get the desired events (two ways to get a number less than three followed by four ways to get a number greater than two--2*4=8). Since we have already shown that there are 36 possible combinations, the probability of our two independent events is 8/36 = 2/9.