Q:       Determine the value of the current Io.

Solution:    We have to determine the value of the current Io. The circuit may be redrawn like

                                        Here from the circuit

                                                             I₁ =-2mA

                                                 I₃ = 1mA

                        By applying KVL for mesh 2

                                    4k(I₂ +I₄ ) +2k(I₂ - I₃) +2k(I₂ - I₁) =0

                                                     8kI₂ +4kI₄ - 2 +4 =0

                                                      4kI₂ +4kI₄ = -1

                        Now applying KVL for loop 4

                                                4k (I₄ +I₂) +2k(I₄ +I₃ ) +6kI₄ -6 =0

                                                                        12kI₄ +4kI₂ +2 -6 =0

                                                                             12kI₄ +4kI₂ -4 =0

                                                                  3kI₄ +1kI₂ =1

            By multiplying equation of mesh2 by 3 and equation of loop 4 by 2 and      subtracting

                                                       12kI₂ +6kI₄ = -3

                                                         -2kI₂ -6kI₄ = -2

                                                                  10kI₂ =-5

                                                                  I₂ = -o.5mA

            Now from the circuit

                                                I₀ = I₁ - I₂

                                                I₀= -2 +0.5 = -1.5mA