To find the domain of the rational function $R(x) = \frac{4x^2 - 16x}{8x^2 - 16x - 64}$, determine which values make the denominator equal to zero and exclude them.

Step 1. Set the denominator equal to zero: $8x^2 - 16x - 64 = 0$.

Step 2. Solve the equation. Begin by factoring out the greatest common factor: $8(x^2 - 2x - 8) = 0$. Then, factor the trinomial: $8(x - 4)(x + 2) = 0$. Apply the Zero Product Property by setting each variable factor to zero: $x - 4 = 0$ or $x + 2 = 0$. Solving these equations gives $x = 4$ and $x = -2$.

Step 3. State the domain by excluding the values found in Step 2. Thus, the domain of $R(x)$ is all real numbers where $x eq 4$ and $x eq -2$.