재이수해야만 is composed of 재 + 이수하다 + 아야만
재 means "again"
이수하다 means "complete (course)"
아야만 means "only if"
재이수해야만 means "only if complete (course) again"
"수학-1 불합격자는 수학-1를 재이수해야만 수학-2로 이동 가능합니다."
Unsuccessful applicants of mathematics-1 course can take mathematics-2 course only if they complete mathematics-1 course again.