I will not solve this system for you, but I will tell you how to do so.
Divide the 2nd equation by 2.
Then add the 3rd equation to each of the other 2.
This will eliminate the x variable and leave you with 2 simultaneous equations in y and z.
In one of the 2 resulting equations the coefficient of the z variable is -4 and the other coefficient of z is -2.
Multiply by two and subtract the 2 equations,
This will eliminate the z variable and leave you with a linear equation in y.
Solve for y and then backtrack to get z and z.