Q:          Determine the value of current I₀.

Solution:  We need to determine the current I₀. To apply KVL the circuit may be redrawn like

                        Here it given

                                                      I₁ = - 2mA

Negative value of I₁ is because the direction of I₁ is going opposite to the Independent current source.

                                                       I₃ =   4mA

                                    Applying KVL for mesh 2

                                    4kI₂ + + 2k(I₂ - I₁) +6k (I₂ - I₃) = 12

                                                    12kI₂ - 24 + 4 =12

                                                I₂ = 32/12k

                                                = 8/3 mA= 2.66 mA

                                                             I₀ = I₂ = 2.66mA