I have went over all the possibilities, but I can not understand why both D1 and D2 be open?



It can not be because D2 is open but the voltage on it is negative (means that it should be closed?)

 

Do you know the KVL ? Also notice that the D1 diode is connected in parallel with (D1+Vz) and from KVL or common sense we know that thinks hooked (connected) in parallel will have the same voltage across them.

 

Write the loop equation for that loop and then solve it for the voltage across one of the diodes. What does the voltage across the other diode have to be in order of the first diode to be on.