Answer: A. $144$

Explanation:1. Understand the function and the given information: The function is $h(x) = (x+p)(x-4)(2x-6)$. The graph of $y=h(x)$ passes through the point $(-6,0)$. This means when $x = -6$, $h(x) = 0$.

2. Use the point $(-6,0)$ to find the value of $p$: Substitute $x = -6$ and $h(x) = 0$ into the function: $0 = (-6+p)(-6-4)(2(-6)-6)$ $0 = (-6+p)(-10)(-12-6)$ $0 = (-6+p)(-10)(-18)$ $0 = (-6+p)(180)$ For this product to be zero, since $180 \neq 0$, the factor $(-6+p)$ must be zero. $-6+p = 0$ $p = 6$

3. Write the specific function for $h(x)$ with the value of $p$: Now that we know $p=6$, the function is: $h(x) = (x+6)(x-4)(2x-6)$

4. Calculate $h(0)$: Substitute $x=0$ into the specific function: $h(0) = (0+6)(0-4)(2(0)-6)$ $h(0) = (6)(-4)(0-6)$ $h(0) = (6)(-4)(-6)$ $h(0) = (-24)(-6)$ $h(0) = 144$

5. Compare with the given options: [A] $144$ [B] $1$ [C] $-6$ [D] $-72$ Our result matches option A.

6. Conclusion: The value of $h(0)$ is $144$.