Learn Russian: Мы хотели обойти опасность, но не смогли. - We wanted to avoid the danger, but we couldn't.

The prefix обо- (a variation of об-) added to a verb of motion means "to go around" an obstacle. Here, it is used figuratively. Instead of literally walking around a physical object, the subjects are "going around" or avoiding an abstract concept like опасность (danger).

Why is обойти in the perfective aspect after хотели?

Verbs of desire like хотеть (to want) can take either aspect, unlike "start/finish" verbs which force the imperfective. Here, the speakers wanted to successfully complete the action of avoiding the danger. Because they focused on achieving a specific, one-time result, the perfective обойти is used rather than the imperfective обходить.

What case is опасность in, and why doesn't its ending change?

It is in the Accusative case because it is the direct object of обойти. Опасность is a feminine noun ending in a soft sign (-ь), meaning it belongs to the 3rd declension. For these nouns, the Accusative form is exactly the same as the Nominative form.

Why do we use the imperfective хотели but the perfective не смогли in the same sentence?

Хотели is imperfective because the desire was a continuous, ongoing state in the past. However, не смогли (from смочь) is perfective because it focuses on the final result: the specific attempt to avoid the danger ultimately failed.