Answer
All values of $h$
Work Step by Step
Multiplying 4 to the first row turns it into [4 12 -8].
Add the two rows together makes the second row [0 $12+h$ 0].
A system is consistent as long as it has at least one solution, in this case, when $h=-12$ the system will have infinitely many solutions; when $h$ is any other number, the system will have exactly one solution. Either way, the system is consistent, so $h$ can be any number.
