I think I understood the content.
The text seems a little bit off with the wording. Instead of saying joint distribution function for definition 11 they should say joint cumulative distribution function
So what they really want if we going by there precise wording is actually the probability mass function of X and Y. Not the cumulative probability mass function. So I am not to sure how to use 12.**
So construct 6 by 6 matrix with X on the y-axis, Y on the x-axis. This matrix is an upper diagonal matrix by definition since X <= Y. (1/6)^r is on the diagonal.
This leaves elements not on the diagonal. To find elements not on the diagonal, make use of the definition of conditional probability,
**It seems 12 only works for joint probability mass function, however the text references joint distribution functions. distribution functions include both probability density functions and probability mass functions.