The phrase "red-handedly" is typically used to describe someone caught in the act of doing something wrong or illegal. Synonyms for this phrase include "caught in the act," "caught red-handed," "in flagrante delicto," and "with one's hand in the cookie jar." These phrases all convey the same idea of being caught in the act of wrongdoing, with no chance of denying or escaping responsibility. Other phrases that could be used as synonyms for "red-handedly" might include "once caught, always guilty," "proof positive," or "smoking gun." Essentially, any phrase or term that conveys the idea of being caught in the act could serve as a synonym for "red-handedly".