Q:  Determine the voltage V₀ .

Solution:          We need to determine the voltage V₀ . The circuit may be redrawn like

                        Here through the circuit

                                                 I₁ = 2mA

            For mesh 2

                                        4k (I₂ -I₃) + 2k (I2 - I₁) = 6

                                       4kI₂ - 4kI₃ +2kI₂ - 2kI₁ = 6 

                                                       6k I₂ - 4kI₃ - 4 =6

                                                            6kI₂ - 4kI₃ = 10

            For mesh 3

                                    6kI₃ + 2k (I₃ - I₁) +4k (I₃ - I₂) = 0

                                     6kI₃ + 2kI₃ - 2kI₁ + 4kI₃ - 4kI₂=0

                                                                12kI₃ - 4kI₂ - 4 = 0

                                                                       12kI₃ - 4kI₂ = 4

                        By solving equations of mesh2 & mesh3

                                                                   24kI₂ - 16kI₃ = 40

                                                             -24kI₂ + 72kI₃ = 24

                                                                             56kI₃ = 64

                                                                                  I₃ = 1.142mA

                        Now to calculate V_O

                                           V₀ =6kI₃

                                          = 6k x 1.142mA =6.85 V