She can't cope with stress.

Literal

She [topic-は] stress [with-に] cope-cannot.

対処する ('cope with / deal with / handle') takes に for the thing being dealt with — different from English 'deal with', which uses a preposition. The pattern follows the broader Japanese tendency to mark the target/topic of mental or relational verbs with に rather than を. The negative potential 対処できない ('cannot cope') is built by appending できない to the noun stem 対処. ストレス ('stress') entered Japanese in the postwar period as a psychology/medical term and now applies broadly to any mental or emotional pressure.