The correct answer is B. supplement.
To supplement something is to add to it in order to make it complete or better. In this case, the man was able to supplement his small income by working in a hotel at night. This means that he was able to earn more money by working a second job, which helped him to make ends meet.
The other options are incorrect because they do not accurately describe what the man did. Option A, amplify, means to make something louder or stronger. Option C, expand, means to make something larger or more extensive. Option D, multiply, means to increase something in number or amount. None of these options accurately describe the man’s actions of working a second job to earn more money.