Meaning
To mess up / To slip up
Example
Desculpe amigão... eu dei mancada interpretando mal a situação.
Sorry man... I messed up by misreading the situation.
Origin
The expression dar mancada comes from mancar, "to limp", which traces back to Latin mancare, from mancus ("maimed, lame"). A mancada is literally a misstep, and many languages tie a stumble of the feet to the idea of erring or failing.
Source: Diário de um Linguista.
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More idioms
Acertar na moscaTo guess correctly / To hit the nail on the headAmigo da onçaA fake/false friendAndar na linhaTo toe the line / To behave properlyArmar um barracoTo cause a public sceneRodar a baianaTo cause a public scene / To go ballisticArrumar sarna pra se coçarTo ask for troubleArrastar as asasTo hit on someone / To flirtAbrir o jogoTo come clean / To open upArregaçar as mangasTo roll up one's sleeves / To get to workAgarrar com unhas e dentesTo hold on for dear life / To seize an opportunity