The correct option is B Carelessly
Antonyms are words which have the opposite meaning in comparison to the other. Option B)carelessly is correct as the word carelessly means in a casual or reckless way; inattentivelyand the word gingerly means in a careful or cautious manner. The other options are wrong as freely, sincerely, and made of ginger mean not under the control of another; as one wishes, in a sincere or genuine way, and using ginger (a plant)respectively. The correct answer is B)carelessly.