Did I do this right? If not, how should I do it?

Unfortunately, your answer is incorrect, but I totally understand your thinking. However, 1/4 is the probability for each individual that they'll be placed in a general civil case. Since there are two of them, and the question is asking the probability that only one will be in a general civil case, you have to approach the problem slightly differently.

There is a 1/16 chance that both will be put in the case (1/4 * 1/4), a 9/16 chance that neither will be put in the case (3/4 * 3/4), and therefore leaving a 6/16 chance that only one of them will be placed in the civil case. (1 - (1/16 + 9/16). This is equivalent to the decimal 0.375.

Draw out a chart of all the 16 possibilities, and circle the ones where the criteria meet. You'll find that there are 6 instances where one of them is put in a general civil case alone.