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I also tried this way and I obtained another result :
By using voltage divider : Vn-Vd=(v0 .R1)/(R1+R2) =(6*2)/12=1 ==> I= 1/2=0.5 A
Is it right ???

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anyone please can tell me if either one of these ways are right or not ???

 

anyone please can tell me if either one of these ways are right or not ???

Your ways are both wrong. In the first case because there is the 10R resistor on the bottom of the battery. In the second case because R1 and R2 are not in series, there are other resistors connected to them.
You have to use nodal analysis to solve it as stated by the question.

 

for my first way:whats the problem with the 10 ohm resistor ,how can it change solving the circuit ???
would you please give me a thread about how can I start here with the nodal analysis ?

 

what about the 2 ohm resistor !!!