Find I_x in the network.
Image from: Irwin, J. David., and R. M. Nelms. Basic Engineering Circuit Analysis, Tenth Edition. N.p.: John Wiley & Sons, 2010. Print.
Solution:
We will find the power in terms of I_x and then solve for I_x at the end. Remember that power is current multiplied by the voltage.
P_{36v}=-36I_xW
P_1=12I_xW
P_2=48W
P_{1I_{x}}=-2I_xW
P_3=56W
We know that there are 2 sources which supply power (they are the red sources, and you can see that the current enters the negative terminal of those sources, which means power is supplied)
Therefore, we can say that the total power absorbed by the other elements must equal the total power supplied by the other 2 elements.
P_{36v}+P_{1I_{x}}=P_1+P_2+P_3
-36I_x-2I_x=12I_x+48+56
Isolating for I_x gives us:
I_x=4A