If the line y - 2 =0 is the directrix of the parabola `x^(2) - ky + 32 =0, k ne 0` and the parabola intersects the circle `x^(2) + y^(2) = 8` at two real distinct points, then the absolute value of k is .

Answer

To solve the problem, we need to analyze the given parabola and circle, and find the absolute value of \( k \) such that the parabola intersects the circle at two distinct points.

### Step-by-Step Solution:

1. **Identify the Directrix**:
The directrix of the parabola is given as \( y - 2 = 0 \), which means the directrix is the line \( y = 2 \).

2. **Rewrite the Parabola**:
The equation of the parabola is given as:
\[ x^2 - ky + 32 = 0 \]
Rearranging this, we get:
\[ x^2 = ky - 32 \]
This can be rewritten in the standard form of a parabola:
\[ x^2 = k(y - \frac{32}{k}) \]
Here, the vertex of the parabola is at \( (0, \frac{32}{k}) \).

3. **Determine the Value of \( a \)**:
From the standard form \( x^2 = 4ay \), we can identify:
\[ 4a = k \quad \text{and} \quad y_v = \frac{32}{k} \]
The distance from the vertex to the directrix is given by:
\[ \text{Distance} = \left| \frac{32}{k} - 2 \right| \]
This distance must equal \( \frac{k}{4} \) (the distance from the vertex to the focus).

4. **Set Up the Equation**:
Therefore, we have:
\[ \left| \frac{32}{k} - 2 \right| = \frac{k}{4} \]

5. **Solve the Absolute Value Equation**:
This gives us two cases to consider:
- Case 1:
\[ \frac{32}{k} - 2 = \frac{k}{4} \]
Multiplying through by \( 4k \) (assuming \( k \neq 0 \)):
\[ 128 - 8k = k^2 \implies k^2 + 8k - 128 = 0 \]
- Case 2:
\[ \frac{32}{k} - 2 = -\frac{k}{4} \]
Multiplying through by \( 4k \):
\[ 128 - 8k = -k^2 \implies k^2 - 8k + 128 = 0 \]

6. **Solve the Quadratic Equations**:
For Case 1:
\[ k^2 + 8k - 128 = 0 \]
Using the quadratic formula:
\[ k = \frac{-8 \pm \sqrt{8^2 + 4 \cdot 128}}{2} = \frac{-8 \pm \sqrt{64 + 512}}{2} = \frac{-8 \pm \sqrt{576}}{2} = \frac{-8 \pm 24}{2} \]
This gives us:
\[ k = 8 \quad \text{or} \quad k = -16 \]

For Case 2:
\[ k^2 - 8k + 128 = 0 \]
The discriminant \( (-8)^2 - 4 \cdot 1 \cdot 128 \) is negative, indicating no real solutions.

7. **Conclusion**:
The valid values for \( k \) from Case 1 are \( k = 8 \) and \( k = -16 \). Since we need the absolute value of \( k \):
\[ |k| = 16 \]

### Final Answer:
The absolute value of \( k \) is \( \boxed{16} \).