I think the third equation should be x-3y+2z=4. There are several ways to solve this system. Let's use elimination and substitution.
(1) 8x-y+z=-46
(2) 3x+2y-3z=-18
(3) x-3y+2z=4
(4)=3(1)+(2)=27x-y=-156
(5)=(1)+(2)+(3)=12x-2y=-60⇒6x-y=-30 (5)
(6)=(4)-(5)=21x=-126, x=-126/21=-6.
6x-y=-36-y=-30, 36+y=30, y=-6; 2z=4+3y-x=4-18+6=-8, z=-4.
SOLUTION x=-6, y=-6, z=-4.