Q:       Determine the value of voltage V_o.

Solution:    we have to calculate the voltage V₀.  The circuit may be redrawn like  

                        V₀ can be given like

                                                V₀ = 2k(I₁ +I₂)

                        Now from circuit

                                                   I₁ = 2V₀/1k

                                                      = 2(2k(I₁ +I₂))/1k

                                                   I₁ = 4(I_{2 +} I₁)

                                                          =4I₁ +4I₂

                                              -3I₁ = 4I₂

                                                 I₁ = -4/3 I₂

            By applying KVL for loop 2

                                      4kI₂ +4k(I₁ +I₂ ) +2k(I₁ +I₂) =6

                                    4kI₂ +4kI₁ + +2kI₁ + 4kI₂+2kI₂ = 6

                                                                  6kI₁ + 10kI2 =6

                                                                    5kI₂ +3kI₁ =3

            As We already calculated

                                                      I₁ =-4/3 I₂

            Therefore

                                                     5kI₂ +3k (-4/3)I₂ = 3

                                                            5kI₂ - 4kI₂ =3

                                                            I₂ = 3mA

            Therefore

                                                          I₁ = (-4/3) I₂

                                                            I₁ =-4mA

            Now from the circuit

                                                        V₀ = 2k(I₁ +I₂)

                                                               = 2k(-4m + 3m)  //putting value of I₁,I₂

                                                         V₀ =-2 V