The correct choice is 'はじめた' (past form of 'はじめる' - to start). The grammar pattern '[Verb Past Form] + とき' (toki) is used here because it describes a past state/action that had already commenced when the subsequent events occurred (experiencing difficulty at the point of having started the part-time job). Sentence context: 'Especially when I started working part-time at the supermarket, I couldn't understand what customers were saying.' 'はじめる' (dictionary form) would imply the period before starting the job, which is incorrect.