How do I define the voltage drops polarity when applying KVL?
Strictly speaking, it's not the sign of the resistors that can be changed, it's the sign (direction) of the current \$I_x\$. Resistors always have positive resistance but you can choose the current in either direction as long as you are consistent.

Suppose you chose \$I_x\$ in the opposite direction. Starting from node \$f\$ and moving counterclockwise, you have a positive voltage across the \$6\Omega\$ resistor, another positive voltage across the \$3\Omega\$ resistor, and a positive voltage across the 12V supply. This gives:

\$I_{x}(6\Omega + 3\Omega) + 12 = 0\$

which results in \$I_{x} = -4/3\$A. The sign is different, indicating that the current actually flows in the opposite direction (i.e. in the original direction shown in the image).

The reason your 4A answer is wrong is that you weren't consistent with the \$I_x\$ direction for the two resistors -- you had \$I_x\$ flowing in the opposite direction through the \$3\Omega\$ resistor.