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Don't get nervous about tomorrow's exam.
Literal
Tomorrow [possessive-の] exam [possessive-の] matter [because/with-で] be-nervous [prohibitive-てはいけません].
The prohibitive construction ~てはいけない / ~てはいけません literally means 'doing X must not be' → 'must not do X.' The noun ことで acts as a fuzzy causal preposition — 'about/over the matter of X.' A caring but firm admonition, probably from a teacher or parent.