Answer
The planes are parallel.
Work Step by Step
Since the normal vector to the plane $2x-4y-z=3$ is $\langle2,-4,-1 \rangle $ and the normal vector to the plane $-6x+12y+3z=1$ is $\langle -6,12,3 \rangle $, one can easily see that
$$\langle -6,12,3 \rangle=-3\langle2,-4,-1 \rangle,$$
That is, the normal vectors are parallel and hence the planes are parallel.
