I calculated
R3 = 1.5K ohms
R2 = 1.5k ohms
VR2 = 3 Volts
VR1 = 2 Volts

I am not sure how to calculate the voltage source of E2. I get confuse with the multiple voltage sources. Can some one explain how voltage goes through this circuit?

 

Hello,

Keep an eye on the direction of the voltage sources.

Bertus

 

I don't know how the direction of the voltage goes, I spend the last 20 minutes searching for how voltage travels but I don't know how they interact with the other voltage sources.

The 4 volts of E1 goes up and gets a voltage drop of 2 volts after R1, so the remaining two volts go into E2. Then there is also the 10 volts of E3 going up into R2 and the voltage drops by 3 volts so 7 volts go into E2. So 2+7=9 volts on E2? I'm pretty sure I am doing something wrong here.

 

You have a simple loop, which makes it easy. Assume a current direction.

Now pick a point on the loop. Any point will do. You will start at that point and work around the loop until you return to the same point.

The voltage across any resistor is found using Ohm's Law. That would be V = I * R.

You sum the voltage drops around the loop. They should all add up to zero.

You can re-arrange and group the variables to solve for the current or any voltage.