The phrase "doeth about-face" means to make a sudden change in direction or opinion. There are several synonyms for this phrase that can be used in different contexts. One synonym is "make a U-turn," which is often used in the context of changing direction while driving or in politics. Another synonym is "flip-flop," which is used to describe someone who changes their opinion frequently or suddenly. "Reversal" is another synonym and can be used to describe a sudden change in policy or decision. "Turnaround" is also a synonym and can be used to describe a sudden improvement or change in fortune.