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Let's go through the question in detail:

### Part a: 
You are asked to find \( h(0) \) where \( h(x) = f(x)g(x) \).

From the table, we have \( g(0) = -8 \). Now, we need to find \( f(0) \) from the graph.

Looking at the graph of \( f(x) \), we can observe that at \( x = 0 \), the value of \( f(0) = -1 \).

Thus,
\[
h(0) = f(0) \cdot g(0) = (-1) \cdot (-8) = 8
\]

### Part b: 
We are asked to find the domain of \( h(x) \), where \( h(x) = f(x)g(x) \).

The domain of \( h(x) \) is determined by the intersection of the domains of \( f(x) \) and \( g(x) \). 

- The graph of \( f(x) \) appears to extend in both directions for all real \( x \), so the domain of \( f(x) \) is all real numbers.
- The table for \( g(x) \) provides specific values, but unless restricted explicitly, \( g(x) \) is also likely defined for all real numbers.

Thus, the domain of \( h(x) \) should be all real numbers, \( (-\infty, \infty) \).

### Part c: 
We are asked to find all \( x \)-values such that \( h(x) = 0 \).

Since \( h(x) = f(x)g(x) \), \( h(x) = 0 \) when either \( f(x) = 0 \) or \( g(x) = 0 \).

- From the graph of \( f(x) \), we can see that \( f(x) = 0 \) at \( x = -2 \) and \( x = 2 \).
- From the table of \( g(x) \), we see that \( g(x) = 0 \) at \( x = -3 \).

Thus, \( h(x) = 0 \) at \( x = -3, -2, 2 \).

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Would you like further explanation on any part of the solution? Here are some related questions you might find helpful:

1. How do you determine the domain of a function from its graph?
2. What is the general approach to solving \( f(x)g(x) = 0 \)?
3. How can we read the values of \( f(x) \) from a graph at specific points?
4. What happens to the domain of a product of two functions?
5. How do we analyze the behavior of functions given in tables and graphs?

**Tip**: When working with products of functions, remember that the product is zero if either of the factors is zero. Always check both functions individually!

Let h(x) = f(x)g(x). Find h(0). What is the domain of h(x)? Find all x-values such that h(x) = 0.

Learn how to solve the function multiplication h(x) = f(x)g(x), including finding h(0), determining the domain of h(x), and identifying x-values where h(x) = 0. This problem covers important function concepts for students in Grades 9-10.

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