Consider a specific moral question which might make it difficult to accept the relativist's response.
First, it might be helpful to point out that a relativistic worldview is a contradiction. If someone says there are no absolutes, is this not an absolute statement? If so, we have a contradiction right off the bat.
Now let me give you an example of a moral issue that might cause a relativistic worldview some problems. As far as I know, there is no culture that prizes cowardice. However, from a relativistic worldview, cowardice is acceptable. If there is a strong feeling against cowardice, then it is going against a relativistic worldview.
Here is another example. Most people would say that child abuse is just wrong. I would agree, but from a strictly relativistic worldview, this too cannot be condemned from an absolute point of view. We can give other examples, like the crime of rape and the protection of the environment. None of these things would be simply wrong in a relativistic worldview.
When considering the relativist's position, remember the stance is oppositional to absolute truths. So, try to consider a moral question where maybe a civil law or code provides a rationale. For example, premeditated murder would present greater difficulty for the relativist over involuntary manslaughter.
When you answer, it is helpful to number the parts of the question so that you organize your response and cover all requirements.