get the hang of

これもAgatha Christieの "Murder in the Mews" からの文章です。
Why a presumably sane young woman should want to fling an expensively-fitted dressing-case into a lake-d'you know, I worried all night because I couldn't get the hang of it.
この "get the hang of" と言う表現も明らかにイディオムで、ここでは "couldn't get the hang of it" で「理由が理解できない」と言うような意味だと推測は付きますが辞書で確認します。
American Herritage Dictionary: Learn the proper way of doing, using or handling something; acquire the knack of something. For example, I finally got the hang of this computer program.
Wiktionary: To learn to handle something with some skill, through practice or diligence, which can lead to an almost unconscious performance thereof. Driving feels awkward when you’re new to it, but it’s easy once you get the hang of it.
Cambridge Idiom Dictionary: to succeed in learning how to do something after practising it After three weeks of using this computer I think I've finally got the hang of it.
辞書の説明だといずれも「コツが分かる」と言う感じ意味ですが小説での意味は余り「コツ」とは関係はなさそうで、引用文と同じような使い方はないかその他の辞書も色々見ました。
OneLook Quick Definitions: a special way of doing something ("He couldn't get the hang of it")
Collins Essential English Dictionary: get the hang of something Informal to understand the technique of doing something
一番簡便な辞書OneLook Quick Definitionsの例と説明 "a special way of doing something" が小説の用法と一番近いと思われます。