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.
https://en.wikipedia.org/wiki/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.