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How can you succeed without a good education?
Literal
Good education [object-を] not-receive-で how succeed can [question-か].
~を受けないで ('without receiving X') uses ~ないで for 'without doing,' the negative te-form for marking accompanying state. どうして ('how, why') + 成功できる (potential of 成功する 'succeed') + か forms a rhetorical challenge: 'How can one succeed if they don't receive good education?'