Answer
The domain is all real numbers except $4$.
$x\ne4$
Work Step by Step
We need to find the value of $x$ that would create a zero in the denominator. We do this by setting the denominator to zero and solving,
$3x-12=0$
Add $12$ to both sides
$3x=12$
Divide by 3
$x=4$
When $x=4$ in this function, there is a zero in the denominator.
$h(4)=\frac{4(4)}{3(4)-12}=\frac{16}{0}$
Therefore the domain can be any number (all real numbers) EXCEPT $4$.
