In an experiment, a four-sided die and a six-sided die are rolled. These dice both have the numbers you would expect on them. Let $Z$ be a random variable that represents the absolute value of the difference. (If a $4$ is rolled and a $1$ is rolled, then $Z=3$.)
What is the probability mass function of $Z$?
For the four-sided die:
For the six-sided die:
I don't know where to go from here. I have an example of this problem using only one die, not two.