expression
Used when the speaker cannot or does not want to specify details, similar to 'something or other' or 'in some way or another'. Often implies a vague, roundabout explanation.
彼は何とかかんとか言い訳をしていた。
He was making some excuse or other.
何とかかんとかして、締め切りに間に合わせた。
Somehow or other, I managed to meet the deadline.
何とか means 'somehow' or 'something' and is more common and less vague than 何とかかんとか, which adds a sense of 'or other' or 'in some roundabout way'.
Reduplicative phrase from 何とか (something or other) with the second part かんとか echoing the pattern, likely from 彼 (か) meaning 'that' in a vague sense.