Equation of plane passes through the points $(1,-1,6),(0,0,7)$ and perpendicular to the plane $x-2 y+z=6$ is
$$
\begin{aligned}
& \left|\begin{array}{ccc}
x-1 & y+1 & z-6 \\
0-1 & 0+1 & 7-6 \\
1 & -2 & 1
\end{array}\right|=0 \\
\Rightarrow \quad & \left|\begin{array}{ccc}
x-1 & y+1 & z-6 \\
-1 & 1 & 1 \\
1 & -2 & 1
\end{array}\right|=0 \\
\Rightarrow & (x-1)(1+2)-(y+1)(-1-1) \\
& +(z-6)(2-1)=0 \\
\Rightarrow \quad 3 x-3+2 y+2+z-6 & =0 \\
\Rightarrow \quad 3 x+2 y+z-7 & =0
\end{aligned}
$$
This plane is passes through $(1,1,2)$.