What Conclusions Can You Draw About The Most Efficient Method Of Extracting Acetic Acid From An Aqueous Solution By Means Of An Immiscible Solvent?

That acetic acid is very hydrophilic. I would not think to do what you mentioned. I would react the solution or rather adjust the pH with NaOH to give Sodium acetate then evaporate some of the water and try to crystalize it out of solution. Does this help?

Solubility of Sodium Acetate: 76 gm/100mls water at 0C