Final answer:
To answer the student's question, the correct choice is D, a balance of -$6. It signifies a debt less than $5 and is a greater integer value compared to a balance of -$12.
Step-by-step explanation:
The student is asking for an example of a balance that has a greater integer value than a balance of -$12 but represents a debt of less than $5. Among the given options, the correct answer is D. A balance of -$6 should be considered, as it represents a debt of less than $5, yet still a greater integer value balance than -$12. In this context, when we talk about a debt represented by a balance, we mean the amount of money that is owed. Therefore, when a balance shows a negative amount, like -$6, it indicates that this is the amount of debt. Since -$6 is a higher integer (less negative) than -$12 and it also indicates a debt of less than $5, it fits the requirements of the question.