Formal/literary. Almost always appears in the negative — 不便置喙 (not appropriate to comment), 无从置喙 (no grounds to comment), 无权置喙 (no right to comment) — as a polite way of saying 'not my place to speak'.
memory
喙 is the beak of a bird. 置喙 literally means 'to insert one's beak' — like the English idiom 'to stick one's beak in.'