I'm assuming you know how to do a system of equations with only two variables, so all you need to do is reduce this system to do that.
I'll label them for convenience.
A) -2x + y +6z = 1
B) 3x + 2y + 5z = 16
C) 7x +3y - 4z = 11
All you need to do multiple and subtract to reduce.
We'll so A - B because it's just he one that occurred to me first. We're getting rid of y's, so we need the constants for y to be the same. Multiple A by 2, so you get:
-4x + 2y + 12z = 2
Now subtract B and you'll have an equation with just x and z.
A-2B = -7x - 3z = -14
Now you need to make a second one. Because it's easiest, do A-C. After that you'll have two equations with just x and z, and you can treat it like a simpler system of equations. Solve for x and z, and then plug those values into any of the equations to find y.
There's a few variations you can take in that process, but that's probably the easiest.