Is superposition theorem the only method to calculate the \$I_0\$ in this circuit?
i want to ask that why should use the superposition theorem to find
  the I0 in this circuit?must we use the superposition theorem to find
  the I0?


No, unless you are instructed to do so.


  i mean is superposition theorem the only method to calculate the I0?


And...


  can we still use some methods to calculate the I0? if yes!can anyone show me how to calculate the I0?


My natural instinct is to simplify....

So, I'd rearrange - the current source is attached to a grounded voltage source - that immediately allows it (the current source) to be moved directly across R3 - this simplifies any analysis because you can turn it into a voltage source of 48 volts in series with 12 kohm (R3).

I'd then rearrange V1, R1 and R2 into a 3 volt source in series with R1||R2 (= 6 kohm). It's simple math to see that the current through R4 flows right to left with a magnitude of 1.5 mA.

Drill down a bit more and the current though R2 is easily found (0.5 mA).

Simulation confirms: -



And, just in case anyone is perturbed by my suggested modification to split the current source from the voltage source and place it across R3: -



Then, convert I1 to a voltage source (I've called it V_I1 below) and rearrange the proper voltage source (V1), R1 and R2 into a source with a single resistor of 6 kohm (named R5) and it's really simple to find the current through R4.



As I said earlier, drilling down a little more finds I_0.