The correct answer is: C. critical.
To cast aspersions on someone’s character is to make negative and unfounded remarks about them. It is a form of slander, which is a false statement that is harmful to someone’s reputation. Critical remarks, on the other hand, can be either positive or negative, and they are often based on facts or opinions.
Option A, cracking, is not a synonym for aspersions. Cracking is a verb that means to make a joke or to say something funny.
Option B, slanderous, is a synonym for aspersions. Slanderous remarks are false and harmful to someone’s reputation.
Option D, throw, is not a synonym for aspersions. Throw is a verb that means to propel something through the air with force.