"카톡한지얼마안됐나봐요?" => 카톡한 지 얼마 안 됐나 봐요? Here's the breakdown of the sentence: - 카톡한 지: 카톡하다(use Kakaotalk) + ㄴ 지 (since..). Since you used Kakaotalk. - 얼마: a short length of time. - 안 됐나 봐요: 안(not) 됐나(it has been) 봐요(it appears). It appears it hasn't been long. => It looks like you haven't been using Kakaotalk very long, doesn't it? It is a half question, expressing a feeling in a question form.

It means "I have the feeling that you are new to Kakaotalk"

roughly translates to "How long has KakaoTalk (KaTalk)" been used that's mostly cause there is no subject such as you but with a subject it would be something like "how long have you been using katalk/how long have you used katalk/for how long ave you used katalk" etcetc...