Answer
\[
0=-2 y+7 z+4 x
\]
Work Step by Step
If the plane $d=a x+b y+c z$ is parallel to the plane
$0=-2 y+7 z+4 x+12, $ with normal vector $\vec{n}=\langle 4,-2,7\rangle$, then the normal vector $\vec{n}$ is also normal to the plane $d=a x+b y+c z .$ This means that $c=7, \quad b=-2$ and $\quad a=4.$ Then
\[
d=a.x+b .y+c. z=4. x-2. y+7 .z
\]
Since this plane passes through the origin $P(0,0,0)=P\left(x_{0}, y_{0}, z_{0}\right)$, we get that
\[
0=d=d=4(0)-2(0)+7(0)
\]
Thus:
\[
0=4 x-2 y+7 z
\]
