When I tried solving it, through simplification of circuits, (correct me if I'm wrong) I got a total resistance of 12k while resistance of Vy is 10k. Upon getting the total resistance, I used the voltage division formula to get E, since the formula is Vx = E(Rx/Rt) where E is the voltage source, Rx is the resistance of x and Rt is the total resistance, I manipulated it to get E, which, in my calculations, is 2.4V. Now this is where I'm confused, since E, which is the source, is less than the voltage of a resistor, did I make a mistake in my calculations? Since, from my understanding, a voltage source's voltage is always greater than the voltage of its elements? Also, can I solve it in the manner of finding Vy first, then Vz, then E? If so, how?
I manipulated it to get E, which, in my calculations, is 2.4V
That's incorrect so, just work from right to left filling out the details as you go: -
No need for any extensive analysis other than using ohm's law and writing things down.
I'm not providing a full answer, just a partial answer so you can see the method.