Let $P(x) = x^3 - 6x^2 - 5x + 4$. Suppose that $y$ and $z$ are real numbers such that
 \[ zP(y) = P(y - n) + P(y + n) \]
for all reals $n$. Evaluate $P(y)$.
1. Given the polynomial \( P(x) = x^3 - 6x^2 - 5x + 4 \), we need to evaluate \( P(y) \) under the condition:
   \[
   zP(y) = P(y - n) + P(y + n)
   \]
   for all real numbers \( n \).

2. First, let \( n = 0 \):
   \[
   zP(y) = P(y) + P(y)
   \]
   This simplifies to:
   \[
   zP(y) = 2P(y)
   \]
   Since \( P(y) \neq 0 \) for all \( y \), we can divide both sides by \( P(y) \):
   \[
   z = 2
   \]

3. Now, substitute \( z = 2 \) back into the original equation:
   \[
   2P(y) = P(y - n) + P(y + n)
   \]

4. Let \( n = y \):
   \[
   2P(y) = P(0) + P(2y)
   \]

5. Calculate \( P(0) \):
   \[
   P(0) = 0^3 - 6 \cdot 0^2 - 5 \cdot 0 + 4 = 4
   \]

6. Substitute \( P(0) = 4 \) into the equation:
   \[
   2P(y) = 4 + P(2y)
   \]

7. Express \( P(2y) \) in terms of \( y \):
   \[
   P(2y) = (2y)^3 - 6(2y)^2 - 5(2y) + 4 = 8y^3 - 24y^2 - 10y + 4
   \]

8. Substitute \( P(2y) \) back into the equation:
   \[
   2P(y) = 4 + 8y^3 - 24y^2 - 10y + 4
   \]
   Simplify:
   \[
   2P(y) = 8 + 8y^3 - 24y^2 - 10y
   \]

9. Recall that \( P(y) = y^3 - 6y^2 - 5y + 4 \). Therefore:
   \[
   2(y^3 - 6y^2 - 5y + 4) = 8 + 8y^3 - 24y^2 - 10y
   \]
   Simplify:
   \[
   2y^3 - 12y^2 - 10y + 8 = 8 + 8y^3 - 24y^2 - 10y
   \]

10. Equate the coefficients of the polynomial:
    \[
    2y^3 - 12y^2 - 10y + 8 = 8y^3 - 24y^2 - 10y + 8
    \]
    Simplify:
    \[
    2y^3 - 12y^2 = 8y^3 - 24y^2
    \]
    \[
    0 = 6y^3 - 12y^2
    \]
    \[
    0 = 6y^2(y - 2)
    \]

11. Solve for \( y \):
    \[
    y = 0 \quad \text{or} \quad y = 2
    \]

12. Evaluate \( P(y) \) for \( y = 2 \):
    \[
    P(2) = 2^3 - 6 \cdot 2^2 - 5 \cdot 2 + 4 = 8 - 24 - 10 + 4 = -22
    \]

The final answer is \( \boxed{-22} \)