Given that
\begin{eqnarray*}&(1)& \text{x and y are both integers between 100 and 999, inclusive;}\qquad \qquad \qquad \qquad \qquad \\ &(2)& \text{y is the number formed by reversing the digits of x; and}\\ &(3)& z=|x-y|. \end{eqnarray*}How many distinct values of $z$ are possible?
1. **Express \( x \) and \( y \) in terms of their digits:**
   Let \( x = \overline{abc} \), where \( a, b, \) and \( c \) are the digits of \( x \). Therefore, we can write:
   \[
   x = 100a + 10b + c
   \]
   Similarly, since \( y \) is the number formed by reversing the digits of \( x \), we have:
   \[
   y = 100c + 10b + a
   \]

2. **Calculate \( z = |x - y| \):**
   Subtract \( y \) from \( x \):
   \[
   x - y = (100a + 10b + c) - (100c + 10b + a)
   \]
   Simplify the expression:
   \[
   x - y = 100a + 10b + c - 100c - 10b - a
   \]
   \[
   x - y = 99a - 99c
   \]
   Factor out the common term:
   \[
   x - y = 99(a - c)
   \]
   Therefore:
   \[
   z = |x - y| = |99(a - c)| = 99|a - c|
   \]

3. **Determine the range of \( a \) and \( c \):**
   Since \( x \) and \( y \) are three-digit numbers, \( a \) and \( c \) must be integers between 1 and 9 (inclusive).

4. **Calculate the possible values of \( |a - c| \):**
   The difference \( |a - c| \) can range from 0 to 8. This is because the maximum difference between any two digits from 1 to 9 is 8 (e.g., \( 9 - 1 = 8 \)).

5. **Determine the distinct values of \( z \):**
   Since \( z = 99|a - c| \), the possible values of \( z \) are:
   \[
   z = 99 \times 0, 99 \times 1, 99 \times 2, \ldots, 99 \times 8
   \]
   This gives us the distinct values:
   \[
   z = 0, 99, 198, 297, 396, 495, 594, 693, 792
   \]

6. **Count the distinct values:**
   There are 9 distinct values of \( z \).

The final answer is \(\boxed{9}\)