If you know the formula for picking a subset of size k from a set
of size n, with replacements allowed, C(n+k-1, k) , it is clear
that there is exactly one order for every set of 6 values. There
are 6 values, and we are picking 6, so the answer is
11 choose 6 = 462.
If you don't know this, we can look at it differently:
The graph on the left is another representation
of the picture in the problem statement. Each column contains a "bar" with height ranging from 1 to 6, representing the value of each die. You will see that the
bars get progressively higher. They cannot go down; otherwise some die has a smaller value than one before it. We can trace the tops
and lefts of the bars in blue, and notice a path that forms. As a matter
of fact, every path going from (0,1) to (6,6) using only ups and rights
will represent a unique result which works. There are 5 ups and
6 rights, and C(11, 6) = 462 ways to order them.
(We just select 6 to be rights, and let the rest be ups)