1Troublesome, burdensome; something bothersome and difficult to deal with — can also refer to a person who causes such trouble.
この手続きは書類が多くて厄介だ。
This procedure is a hassle because it requires so many documents.
パソコンが急に動かなくなって厄介なことになった。
The computer suddenly stopped working, which turned into a real headache.
彼はいつも厄介な質問ばかりしてくる。
He's always asking troublesome questions.
この染みはなかなか取れなくて厄介だ。
This stain is hard to remove, which is annoying.
2Being taken care of by someone, or imposing on someone's kindness — used in set phrases like 厄介になる (to be indebted to someone's care) and 厄介をかける (to trouble someone).
大学生の間、叔父の家に厄介になっていた。
While I was a university student, I was taken care of at my uncle's house.
いろいろとご厄介をおかけしました。
I'm sorry for causing you so much trouble.
困ったときはお互いに厄介になり合うものだ。
When times are tough, people rely on and impose on each other.