Answer:

The above network can be considered as cascade connection of two networks $N_1$ and $N_2$.

The network $N_1$consists of $2 \Omega $ resistor , $2H$ inductor and $2F$ capacitor.

Applying KVL to mesh 1 of network $N_1$,

$V_1=\bigg(2+\dfrac{1}{2s}\bigg)I_1+\dfrac{1}{2s}I_2$.............................(1)

Applying KVL to mesh 2 ,

$V_2=\dfrac{1}{2s}I_1+\bigg(2s+\dfrac{1}{2s}\bigg)I_2$.............................(2)

From (2) we have 

$I_1=2sV_2-(4s^2+1)I_2$..................................(3)

Substituting (3) in (1),

$V_1=\bigg(2+\dfrac{1}{2s}\bigg)\bigg[2sV_2-(4s^2+1)I_2\bigg]+\dfrac{1}{2s}I_2$

$V_1=(4s+1)V_2-(8s^2+2s+2)I_2$

On comparing with the ABCD paramter equation , we get 

$ \begin{bmatrix} A_1 &B_1 \\[0.3em] C_1 & D_1 \\[0.3em] \end{bmatrix}= \begin{bmatrix} 4s+1 & 8s^2+2s+2 \\[0.3em] 2s & 4s^2+1 \\[0.3em] \end{bmatrix} $

The network $N_2$ consists of the parallel combination of $1F$ capacitor and $1 \Omega $ resistor,

Applying KVL to the mesh 1 , 

$V_1'=\dfrac{1}{s+1}I_1'+\dfrac{1}{s+1}I_2'$......................(4)

Applying KVL to mesh 2 ,

$V_2'=\dfrac{1}{s+1}I_1'+\dfrac{1}{s+1}I_2'$.......................(5)

From (5)

$I_1'=(s+1)V_2'-I_2'$...............................(6)

Also , $V_1'=V_2'$......................................(7)

Comparing (6) and (7) with ABCD paramter equations , 

$ \begin{bmatrix} A_2 &B_2 \\[0.3em] C_2 & D_2 \\[0.3em] \end{bmatrix}= \begin{bmatrix} 1 & 0 \\[0.3em] s+1 & 1 \\[0.3em] \end{bmatrix}$

Hence , overall ABCD parameters are

 $ \begin{bmatrix} A &B \\[0.3em] C & D \\[0.3em] \end{bmatrix}= \begin{bmatrix} 4s+1 & 8s^2+2s+2 \\[0.3em] 2s & 4s^2+1 \\[0.3em] \end{bmatrix} \begin{bmatrix} 1 & 0 \\[0.3em] s+1 & 1 \\[0.3em] \end{bmatrix}$

$ \begin{bmatrix} A &B \\[0.3em] C & D \\[0.3em] \end{bmatrix}= \begin{bmatrix} 8s^3+10s^2+8s+3 & 8s^2+2s+2 \\[0.3em] 4s^3+4s^2+3s+1 & 4s^2+1 \\[0.3em] \end{bmatrix} $