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.