Q:       Determine the value of current Io.

Solution:    we have to calculate the current I₀.  The circuit may be redrawn like  

                                    Here from the circuit

                                                 I₁ = 2mA

                                                 I₂ = - 4mA

            By applying KVL for loop 3

                                         2kI₃ + 1k (I₃ - I₂) + 2k(I₃ + I₁ - I₂) =12

                                      2kI₃ -1kI₂ + 1kI₃ + 2kI₃ +2kI₁ - 2kI₂=12

                                                                         5kI₃ -3kI₂ + 2kI₁= 12

                                                                              5kI₃ + 12 + 4 = 12

                                                                                                5kI₃= - 4

                                                                                                    I₃ = - 4/5 = .8mA

                        Now from the circuit

                                                            I₀ = I₃ + I₁- I₂

                                                                             = -.8 +2 +4 //put the value in equation

                                                            I₀ = 5.2 mA