What does 결자해지 (結者解之) mean?

Answer: One who ties a knot must untie it./Solve the problems you yourself create.

결자해지 (結者解之) literally means "One who ties a knot (結者) unties (解) it (之)." In other words, the one who creates a problem should solve it.

結 (결) is the Chinese version of the pure Korean verb 맺다, whose first definition is to knot or to tie [a knot]. In addition, the Chinese character 結 (결) can be used to mean the noun knot (매듭). The Chinese character 解 (해) is the Chinese version of the pure Korean 풀다, which means to untie or to solve.

Besides meaning to knot or to tie, 맺다 or 結 (결) can also mean the following, according to Donga's PRIME Korean-English Dictionary:

• to bear/to produce [fruit/results]: 열매를 맺다 or 결실(結實) / 결과(結果)
• form [a relationship]: 관계를 맺다. or 결교(結交)하다
  form [a friendship]: 우정을 맺다. or 결교(結交)하다
  make [a promise]: 약속을 맺다. or 결약(結約)하다
  make [a contract}: 계약을 맺다. or 결약(結約)하다
  make {a treaty]: 조약을 맺다.
  combine: 둘 이상의 것이 서로 관계를 맺고 합쳐서 하나로 됨: 결합(結合)
• finish, end, conclude [a speech]: 연설을 맺다.
  an epilogue: 끝맺은 말 or 결문(結文)
• harbor, bear, cherish [a grudge]: 원한을 맺다 or 결원(結怨)

By the way, the Korean word for marriage is 결혼 (結婚), which literally means to form (結) a marriage (婚), so you would not say 결혼을 맺다 since the meaning for 맺다 is already in the character 結 (결) in 결혼 (結婚).  Instead, you would just say or write 결혼하다. You could, however, say 백년 가약을 맺다, which is a wedding vow that means to pledge one's eternal love. Actually, the literal meaning is to make a beautiful promise (가약 佳約) for 100 years, so it is not actually for eternity, thank Goodness.