Your choice (distillation) is

But before doing distillation, we must remove inorganic impurities and water from the organic phase.

After back extraction from the aqueous solution, the organic phase contains small amounts of water and inorganic compounds (in this case NaOH and NaCl). You need to remove the inorganic impurities, then the water from the organic solution.

First, let's wash* the organic solution to remove inorganic impurities.

Which liquid will you use?

methanol
brine (saturated NaCl)
water