Answer
The solution set is
${((6-2t , \frac{5t-18}{2} , \frac{9t-18}{2} , t)|t\in\Re)}$
Work Step by Step
System
${y-z+2w=0}$
${3x+2y+w=0}$
${2x+4w=12}$
${-2x-2z+5w=6}$
Start with the augmented matrix row echelon form (Gauss-Jordan) as shown in the image below