Answer
All real numbers apart from $2$ and $-\frac{4}{3}$.
Work Step by Step
We know that for rational expressions the domain is all the real numbers, excluding when the denominator is $0$.
$3x^2-2x-8=3x^2-6x+4x-8=3x(x-2)+4(x-2)=(x-2)(3x+4)$
Here the denominator is $0$, when $x=2$ or $x=-\frac{4}{3}$, thus the domain is all real numbers apart from $2$ and $-\frac{4}{3}$.
