Determine the z parameters of two port network
You seem to be going about this haphazardly - consider a very simple two port network and it's formulas as shown below: -



Look at the impedance term in the top left (R1 + R2). It basically tells you this: -

$$V_{IN} = I_{IN}\cdot (R1 + R2)$$

So, in your circuit (with the dependent source) you have to find the equivalent i.e. what is \$I_{IN}\$ based on the input \$V_{IN}\$. Simple observation will tell you that \$I_{IN}\$ is: -

$$\dfrac{-(4Ω + 2Ω)}{3\cdot V_{IN}} = \dfrac{-2}{V_{IN}}$$

So the impedance is -2Ω in the top left position.

Can you take it from here?