i think it would be quite a bit a challenge to explain how it works in a sentence. as for me, you should take it as kinda phrasal expression. please don't take out "기" as in "~이기는 하지" because the word "기" itself doesn't make sense. although there might be a reasonable explanation grammatically, i think it isn't a good idea. i recommend you should memorize "~이기는 하지" as one expression. as your sentence, the expression "~이기는 하지" is often followed with "방법", and it is used when you have to admit that somebody has a good idea on something, but you don't agree pretty much and you won't take it because you believe you have got a better option or idea. here are some examples of its usage 그건 좋은 방법이긴 하지.. 그런데 내생각은 조금 틀려 that might be a good idea, i have to admit it, but i have got an better idea. "이긴 하지" is a short form of "이기는 하지" and more common in spoken Korean. also you can drop "방법" as in " 방법이긴 하지". "그건 좋긴 하지, 그런데 내생각은 조금 틀려"