Solution:

Given: X X X XY Y Y YZ Z Z Z................Y X X X Z

To find: The values of X, Y, and Z

Let's analyze the given pattern step by step:

1) The pattern starts with three consecutive X's, followed by a Y, then three consecutive Y's, followed by a Z.
2) The pattern then repeats with three consecutive Z's, followed by a Y, then three consecutive X's, followed by a Z.

From this analysis, we can conclude the following:

1) The value of X is the same as the number of consecutive X's at the start of the pattern.
2) The value of Y is the same as the number of consecutive Y's after the first X in the pattern.
3) The value of Z is the same as the number of consecutive Z's after the first Y in the pattern.

Now let's apply this analysis to the given options one by one:

a) X=9, Y=2; Z=8

If X=9, it means there are 9 consecutive X's at the start of the pattern. But we can see that there are only 3 consecutive X's at the start. Thus, option a) is incorrect.

b) X=9, Y=1; Z=9

If X=9, it means there are 9 consecutive X's at the start of the pattern. But we can see that there are only 3 consecutive X's at the start. Thus, option b) is incorrect.

c) X=8, Y=1; Z=8

If X=8, it means there are 8 consecutive X's at the start of the pattern. But we can see that there are only 3 consecutive X's at the start. Thus, option c) is incorrect.

d) X=9, Y=1; Z=8

If X=9, it means there are 9 consecutive X's at the start of the pattern, which is correct.
If Y=1, it means there is 1 consecutive Y after the first X in the pattern, which is correct.
If Z=8, it means there are 8 consecutive Z's after the first Y in the pattern, which is correct.

Therefore, option d) is the correct answer.

In conclusion, the correct values of X, Y, and Z in the given pattern are: X=9, Y=1, and Z=8.