What did Sam do regarding his offer to help?

The choice that indicates Sam's reaction to the offer to help is that he flatly refused to lend a hand. This accurately reflects a situation where someone decisively turns down an offer, suggesting a clear and firm stance against providing assistance. The use of the word "flatly" emphasizes the unequivocal nature of his refusal, indicating that there was no room for negotiation or reconsideration in his response.

In contrast, the other options suggest varying degrees of agreement or acceptance which do not align with the notion of refusal. For instance, "flatly agreed to help" and "flatly accepted to assist" imply a willingness to accept an offer, which directly contradicts the idea of refusal. Meanwhile, "flatly promised to help" suggests a commitment to provide help, again contrary to the refusal that Sam exhibited. Thus, option B stands out as the only answer capturing Sam’s action of declining assistance, accurately reflecting the context of the situation.