Learn Russian: Заходя в древний храм, мы увидели колонны, разрушенные во время войны. - Stopping by the ancient temple, we saw columns destroyed during the war.

The word разрушенные is a past passive participle. It acts as an adjective to replace the full clause которые были разрушены (which were destroyed). Because it directly modifies колонны, it attaches right after the noun and takes the same plural ending.

Why does разрушенные have a double -нн- here?

Full past passive participles formed from perfective verbs, like разрушить, are spelled with a double -нн-. If you expanded this back into a который clause using the short-form participle (которые были разрушены), it would drop to a single -н-.

Why is the imperfective verbal adverb заходя used instead of the perfective зайдя?

Заходя expresses simultaneous action: we saw the columns while we were in the process of entering. If the sentence used the perfective form зайдя, it would mean we saw the columns only after we had completely entered the temple.

What case is разрушенные in?

It is in the accusative case, agreeing completely with колонны. Since колонны is the direct object of увидели (we saw), it takes the accusative. Because it is an inanimate plural noun, its accusative form looks exactly like the nominative, and the participle разрушенные follows the exact same pattern.