Q:       Calculate the voltages V_ad , V_ac and V_bd.

Solution:          We need to calculate V_ad & V_ac. The circuit may be redrawn like

            As seen from the circuit there is only a voltage source among points a & d therefore the voltage V_ad will be 12 V. There is no physical closed loop between point a & c we may consider two closed loop acba & acda.

            By applying KVL equation for the loop acba

                                                V_ac - 4 - 6 = 0

                                                V_ac = 10 V

            Second loop in which only unknown value is Vac is acda. KVL equation for this  loop will be

                                                V_ac + 2 - 12 =0

                                                V_ac = 10 V

                                           Calculate the value of V_bd yourself.