Let me _ the candle from the cake.

Explanation

'Switch-off' means stopping the flow or operation of something by means of a tap, switch, or button. A candle does not operate via a switch; hence incorrect. 'Blow out' means being extinguished by an air current. This is correct, as candles are unlightened by the strong passage of air. 'Extinguish' means putting an end to; destroying and, in this case, can be used in the context of a large flame, but not a candle. 'Eliminate' means completely remove or get rid of (something), which is incorrect in this case.