You toss two 6-sided dice one right after the other. What is the probability of rolling a 3, then rolling a different odd number on the next toss?

Well, the first thing you need to do to solve this problem is to find the probability of rolling a three. In other words, how many possible outcomes are there where you roll a three? The answer you get should be $\frac{1}{6}$.
Next, we need to find the probability that you will roll an odd number that is not 3. On the average 6-sided number cube, there are 2 odd numbers other than 3, so you should get $\frac{2}{6}$.
Finally, add together these two probabilities. You should get $\frac{3}{6}$, or $\frac{1}{2}$.