Add the first equation to the second one; subtract the first equation multiplied by 2 from the third one:

x + y + z = 12

3y +4z = 56

-3y -2z =-40

Add the second equation to the third one:

x + y + z = 12

3y +4z = 56

2z = 16

Then from the third equation z = 16/2 = 8, from the second equation y = (56-4z)/3 = (56-32)/3 = 24/3 = 8, from the first equation x = 12 - y - z = 12 - 8 - 8 = -4.