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She breaks a dish every time she does the washing up.
Literal
She [topic-は] dishwashing [every time-のたびに] plate [object-を] breaks.
~たびに means 'every time' — attached to a noun with の (洗い物のたびに) or directly to a verb dictionary form (洗うたびに). The habitual present tense 割る implies this is a recurring pattern. 洗い物 means 'the washing up' or 'dishes to be washed' — the ~物 suffix turns a verb stem into 'things related to that action.' There's a wry humor here: she is reliably, predictably clumsy.