Q:  Determine voltage across 2k ohm resistor.

 Solution:

Joint 2k & 2k and then

For node (1)

                        V₁/3k +4mA +2mA + (V₁-V₂) /6k =0

                                       2V₁ +12 +V₁₊24 - V₂ =0

                                       -V₂ + 3V₁ = -36

For node (2)

              V₂/4k + V₂/12k - 2mA +(V₂ -V₁)/6k = 0

                3V₂ +V₂- 24 + 2V₂ - 2V₁ = 0

                             6V₂ - 2V₁ = 24

By addition     

          9V₂ - 3V₁ =36

          -V₂ + 3V₁ =-36 

                      8V2 =0

                       V2 =0

From the circuit on the right side two resistances are in series i: e 2k & 2k ohm therefore we can apply voltage divider rule here

                                                               V₀ = 2/4 x V2

                                                                             = 2/4 x 0  = 0             Ans.