To find the domain of the rational function $R(x) = \frac{2x^2 - 14x}{4x^2 - 16x - 48}$, follow the standard procedure to exclude values that cause division by zero:

Step 1. Set the denominator equal to zero: $4x^2 - 16x - 48 = 0$. Step 2. Solve the equation by factoring out the greatest common factor and then factoring the trinomial: $4(x^2 - 4x - 12) = 0$ $4(x - 6)(x + 2) = 0$ Using the Zero Product Property, set each variable factor to zero: $x - 6 = 0$ or $x + 2 = 0$. Solving these equations yields $x = 6$ and $x = -2$. Step 3. The domain is all real numbers excluding those values. Therefore, the domain of $R(x)$ is all real numbers where $x eq 6$ and $x eq -2$.