-도록 combines with the verb. An example that -도록 is used as 'while'. 이 지경이 되도록 뭐했어? What did you do while it turned out to be like this? 한 달이 넘도록 서로 말 한 마디도 안 해. We(or they) don't speak of a single word to each other as a month passes by. >> You can use it to say something you think it could have been better(if they dealt with the matter or tried to make up). So it sounds a bit stronger than -는 동안. ShinDonggeun's examples show how it's used as '(to make) someone do something'. Like the 'do' verb of English, 하다 has many meanings as well, -도록 하다 is the whole form that means 'to make someone do something'. It's more formal than -게 하다. -토록 is used with a noun and then it becomes an adverb. 영원토록 forever (usually heard from a song) 이/그토록 like this/that 그토록 보고 싶었던 바다에 갔다. I went to the sea that I had wanted to see so badly. I can't think of any other nouns that can be used with -토록, I suppose there aren't many ones in this case.

It is similar to the passive form. 오디션에서 배우들은 즉석에서 연기를 하도록 요구받았다. At the audition, the actors were asked to perform upon the place. 개는 그렇게 하도록 배웠다. The dog is taught to do so. 엄마는 나에게 법률 공부를 하도록 했다. My mother urged me to study law. 내가 오늘 개회사를 하도록 해주세요. Let me open a meeting today. There are other mening but it's difficult to explain in English.