The odd-shaped dotted red box defining the supernode is not part of the original diagram but was added later during the solution.

Define the dependent source parameters in terms of node voltages.

I₁ = (V_A - V_B) / 1K

V₂ = V_B

The 12 volts source directly connects node C to node B.
The 15 volt source directly connects node B to the reference node.
The dependent voltage source 6K I₁ directly connects the reference node to node A.

Thus: Node C is connected to Node B is connected to the reference node is connected to Node A using ONLY voltage sources, so ALL essential nodes are in a huge supernode.

Next express the value of each voltage source involved in forming the giant supernode in terms of the node voltages.

First the dependent source:

6K I₁ = V_A

Inserting the expression for I₁ from above gives

6K (V_A - V_B) / 1K = V_A

This simplifies to

5 V_A - 6 V_B = 0 (eq. 1)

Next the 12 volt source:

V_C - V_B = 12 (eq. 2)

Finally the 15 volt source:

V_B = 15 (eq. 3)

At this point you might notice that we have 3 equations and 3 unknowns, thus it appears that we need no more equations. Checking the nodal analysis algorithm, it says to write KCL at any remaining simple essential nodes (except reference) and at all supernodes which do not include the reference node. Since there are no remaining simple essential nodes and the only supernode includes the reference node, there are NO KCL equations to write.

Solving:

We already know from eq. 3 that

V_B = 15 V

Inserting this into eq. 2 gives

V_C - 15 = 12

V_C = 27 V

Inserting 15 into eq. 1 for V_B gives

5 V_A - 6 (15) = 0

5 V_A = 90

V_A = 18 V