Answer: B. $0$

Explanation:1. Understand the Zero Product Property: If the product of several factors is zero, then at least one of the factors must be zero. The given equation is $4x(x-3)(x+9)=0$. The factors are $4x$, $(x-3)$, and $(x+9)$.

2. Set each factor equal to zero and solve for x: Factor 1: $4x = 0$ Divide by $4$: $x = \dfrac{0}{4} \Rightarrow x = 0$

Factor 2: $x-3 = 0$ Add $3$ to both sides: $x = 3$

Factor 3: $x+9 = 0$ Subtract $9$ from both sides: $x = -9$

3. List all solutions: The solutions to the equation are $x=0$, $x=3$, and $x=-9$.

4. Identify one solution from the given options: [A] $-3$: Not a solution. [B] $0$: Is a solution. [C] $4$: Not a solution. [D] $9$: Not a solution.

Conclusion:One of the solutions to the given equation is $0$. (The other solutions are $3$ and $-9$.)