Answer:
sorry mam I cant ans this question cuz I also dk if u get this ones ans tell me even n im aorry
The correct answer is A. Pat hung her head without speaking a word.
Indirect characterization means that a character is described implicitly - the author did not directly say what a character is like, but rather we as readers have to infer based on their behavior and what they say. Therefore, C is incorrect because that is direct characterization; and B and D are incorrect because they are not characterization at all. Based on A, we can infer that Pat is sad or upset, which is why (s)he is described indirectly.
To do math homework, you gotta show us a picture and we can help you step by step, please, if you time edit your question and take a picture and I will guide you through it. :)
A. The sentence works fine. one could argue B, but a colon is used to separate a run-on or show two complete thoughts in the same sentence, so arguably B would not work either.