4x + 4y + z  = 24,    (1)
2x - 4y + z  =  0,    (2)
5x - 4y - 5z = 12.    (3)

First, distract (1) from (2). Second, multiply (1) by 5 (both sides) and then add to (3). 
In this way you eliminate z and obtain the system for two unknowns x and y:

-2x -  8y = -24,      (4)
25x + 16y = 132.      (5).

By continuing with the elimination method, multiply (4) by 2 (both sides) and then add to (5). You will get 

21x = 132 - 48 = 84.

Hence, x =  = 4.

Next find y from (4) and then restore z from any of (1), (2) or (3).