Answer
Av = v2/v1=-0.18
Work Step by Step
Let I1 be the left hand mesh, I2 be the middle mesh, and I3 be the right hand mesh. All mesh currents are clockwise in direction.
Note that
For mesh #1:
v1-I1-2(I1-I2)=0
For mesh #2:
-2(I2-I1)-4I2-4(I2-I3)+2v1=0
For mesh #3:
-2v1-4(I3-I2)+4I3=0
and finally, v1=2(I1-I2)
Solving,
I1=0.455v2
I2=0.182v2
I3=0.045v2
but v2=4I3=4*0.045v2
or Av = v2/v1=-0.18
