What is the correct word for this sentence: No, we _____ finish our homework first?

The correct word to complete the sentence "No, we _____ finish our homework first" is "should." This term conveys a sense of obligation or recommendation, indicating that finishing homework is necessary before proceeding to another activity. The use of "should" suggests that it is advisable or expected to complete the homework, reflecting a common understanding of priorities in tasks or responsibilities.

In the context of the other options, "could" implies possibility, but does not express the necessity of finishing the homework first. "Must" indicates a strong obligation, which might suggest there is no alternative; while this could also fit in some contexts, it carries a more forceful connotation. "Would" suggests a conditional or hypothetical situation, often indicating what one might do under certain circumstances, which does not align with the clear directive implied by the sentence structure. Thus, "should" is the most appropriate choice for conveying the idea of obligation balanced with flexibility.