From 3rd equation: y=-6-5z. Substitute for y in other two equations:
2x+6+5z+3z=-12; 2x+8z=-18; (A) x+4z=-9.
-x-12-10z-3z=15; (B) -x-13z=27.
Add A and B: -9z=18, z=-2; so x=-9-4z=-1 and y=-6-5z=4.
CHECK:
-2-4-6=-12 OK; 1+8+6=15 OK; 4-10=-6 OK
So solution is x=-1, y=4, z=-2.