Okay, so you need to find the domain. You need to show that there cannot be an answer with a denominator of 0.
So, let's evaluate the denominator:
4 - √(6x - 38)
This cannot be equal to 0 , so let's solve for zero and find where the solution does not exist.
4 - √(6x - 38) = 0
4 = √(6x - 38)
16 = 6x - 38
6x = 54
x = 9
So, at x = 9, there is not solution, therefore the domain is:
x = the set of all real numbers except x = 9