Understanding the Correct Answer: "might"
In the sentence "We __________ take a detour before we reach the destination," the correct option is "might." Let's explore why this is the case.

Possibility and Uncertainty
- The word "might" expresses a possibility or uncertainty about an action.
- Using "might" suggests that taking a detour is not guaranteed but is a potential option under certain circumstances.

Comparison with Other Options
- **would**: This implies a strong intention or willingness to take the detour. However, it doesn't convey uncertainty, which is essential in this context.
- **should**: This indicates a recommendation or obligation. It implies that taking a detour is advisable, but again, it lacks the element of possibility.
- **will**: This word suggests a definite future action. It indicates certainty, which does not fit the context of the sentence as it is about an uncertain situation.

Contextual Relevance
- The sentence hints at an option rather than a commitment. Therefore, "might" is the most suitable choice.
- It leaves room for other possibilities, acknowledging that a detour may or may not occur.

Conclusion
In summary, "might" is the best answer because it encapsulates the idea of a potential detour without asserting any certainty or obligation. It perfectly fits the context of the sentence, making it the correct choice.