expression
this and that; something or other; one thing or another
Used to refer vaguely to various unspecified things, often in contexts of doing or talking about multiple miscellaneous matters.
何かかにかと忙しくて、返事が遅くなった。
I was busy with this and that, so my reply was late.
彼は何かかにか理由をつけては、会議を欠席する。
He always finds one thing or another as an excuse to skip meetings.
あれこれ is more common and casual for 'this and that'; 何かかにか is slightly more formal or literary.
何やかや is similar in meaning but more colloquial; 何かかにか can sound a bit more deliberate.
Reduplicative phrase combining 何か (something) and かにか (an old interrogative pattern); the exact derivation of かにか is uncertain, but it likely served as a rhyming or emphatic counterpart.