-ㄹ 수 있다 vs. -도 되다
My guess is that -ㄹ 수 있다 is the physical ability to do something, and -도 되다 is the re-assurance that it is okay to do what the receiver is about to do. 맞아죠?

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맞아죠? should be 맞죠?

And, yes you're right! ㄹ 수 있다 means you have the ability to do something and -도 되다 is asking if/letting someone know if something is okay to do or not. ^^

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"-ㄹ수 있다" means "to be able to",
"-도 되다" means "to be allowed to"

나는 책을 읽을 수 있다. I can read a book.
너는 이제 집에 가도 된다. you can (or may) go home now.

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-ㄹ 수 있다 means "able"
-도 되다 means "allow"