Find the domain of the following rational function. \[ H(x)=\frac{-8 x^{2}}{(x-6)(x+8)} \]

Step 1 ：Define the function \(H(x)=\frac{-8 x^{2}}{(x-6)(x+8)}\).

Step 2 ：The domain of a function is the set of all possible input values (often the 'x' variable), which produce a valid output from a particular function.

Step 3 ：For a rational function, the domain is all real numbers except those that make the denominator equal to zero, because division by zero is undefined.

Step 4 ：In this case, the denominator of the function is \((x-6)(x+8)\). Therefore, the values of x that make the denominator equal to zero are x = 6 and x = -8. These are the values that we need to exclude from the domain of the function.

Step 5 ：The values that make the denominator equal to zero are x = -8 and x = 6. Therefore, the domain of the function H(x) is all real numbers except -8 and 6.

Step 6 ：\(\boxed{\text{The domain of the function is } x \in \mathbb{R} \text{ such that } x \neq -8 \text{ and } x \neq 6}\)