Calculate the current
Your professor's \$V_x =-6V\$ calculation is right. But \$ Is \$ is wrong.







simulate this circuit &ndash; Schematic created using CircuitLab

What you have to do first is - To mark current directions as per the sign conventions assumed for voltage drops on resistors. These directions may or may not be the actual directions of the currents, which will be clear after calculations based on the assumptions made.

Apply Kirchoff's current law at A:
$$4V_x + I_s +I_{R3} = I_{R2}$$
$$4V_x + I_s +\frac{V_x}{4} = \frac{8}{2}$$

On solving, \$I_s = 29.5A\$

\$I_{R3}\$ is obtained as -1.5A. The meaning of this is:

Current through 4ohm resistor, \$I_{R3}\$ has a magnitude 1.5A. However its direction is actually in the opposite direction to what we assumed during calculations.