How to calculate Vo in this circuit?
Neither answer is correct, but you mostly had the right idea.

You correctly calculated the current through the whole circuit: \$\dfrac{10 - (-2)}{2000 + 4700} = 1.791 mA\$

The next step you could take would be to calculate the voltage drop across each resistor:


Across the 2K resistor: 2000 * 0.001791 = 3.58 V
Across the 4.7K resistor: 4700 * 0.001791 = 8.42 V


To find the voltage at Vo, start at either end and add or subtract the voltage drop across the resistor.


If we start at the 10V end: Vo = 10 - 3.58 = 6.42 V
If we start at the -2V end: Vo = -2 + 8.42 = 6.42 V