1. \Х-50 (кому) disapprov ( impers or with subj: human one or s.o. is completely indifferent to, unconcerned about etc sth. : X-y (X) хоть бы хны - X couldn't (could) care less
X doesn't care (at all (in the least etc ))
X doesn't give a damn (a hoot, a darn etc)
it doesn't mean a thing to X. "(Ты) мог бы встретить, - капризно и запальчиво выкрикивала она сквозь слёзы. - Думала, не дойду, думала, упаду, а... ему хоть бы хны» (Распутин 2). "You could have met me," she cried through her tears crankily. "I thought I wouldn't make it, I thought I would fall, and...you don't care!" (2a).
2. — кому (impers) sth. does not affect or cause any reaction in s.o. : X-y хоть бы хны - it doesn't bother (ruffle) X a bit (at all)
it has little (no) effect on X
X doesn't turn a hair
(in refer, to physical sensations, usu. pain) X doesn't even feel it.
Один человек, допустим, такой это весёлый-весёлый, что с ним хоть что ни случись - ему хоть бы хны, плюнет и дальше жить пойдёт (Попов 1). One person, let's say, is so cheerful and jolly that no matter what happens to him, it doesn't bother him a bit, he just shrugs it off and goes on living (1a).
«Ты её (тётушку Хрисулу) трахнул фасолевой подпоркой, а ей хоть бы хны?!» - сказал Чунка, не глядя вниз (Искандер 5). "You bonked her (Auntie Chrysoula) with a beanpole, and she didn't even feel it?" Chunka said without looking down (5a).
Большой русско-английский фразеологический словарь. — М.: ACT-ПРЕСС КНИГА. С.И. Лубенская. 2004.