Left: Battery connection in series
E1 + E2 = I*R1 + I*R2 + I*R3
3 + 9 = 2 + 3.23 + 6.67
12 = 11.9
Electrons flow from a minus of 3V battery
Right: Battery connection is oncomming:
E1 - E2 = I*R1 + I*R2 + I*R3
I = (E1-E2) / (R1 + R2 + R3)
I = -6 / 1800 = - 0.003 A = - 3.33 mA
Electron go from a minus of 9V battery.
Minus means we chose a wrong direction of counting the minuses and pluses.