Q: Determine current passing through 4k ohm resistor.

Solution:

                        For node 1

                                     (V₁-1₂)/12k + V1/6k + (V₁+6) /4k = 0      // V=IR

                                                V₁+ 3V₁  - 12 + 3(6) +2V₁= 0

                                                         6V₁ = -6

                                             V₁= (-6/6) = -1 volt

                                       I_o = (V₁ - (-6))/4k

Here negative sign along -6 is because of the negative reference of the   battery

                       Hence             I_o= (-1+6)/4k

                                            = 5/4 =     1.2mA       Ans.