The given plane is $3x+6y-z+12=0$
Converting the eqn. into intercept form $\large\frac{x}{-4}+\frac{y}{-2}+\frac{z}{12}=1$
The intercepts of this plane are $ (-4,-2,12)$
The intercepts of the required plane are $(-8,-4,24)$
$\therefore\:$ The eqn. of the required plane is $\large\frac{x}{-8}+\frac{y}{-4}+\frac{z}{24}=1$
$i.e.,\:\:3x+6y-z+24=0$