how to delete the nanny knows best discovery quest in the sims freeplay.

You can't

Only option is to not start the quest, by never talking to the nanny in the park

Once you have started it, it must be done. You can of course not do it and forfeit the time limited prize, however as it is it a Discovery quest, you can not start another discovery quest until the current one is completed. 

You also have the option of not having a current discovery going by not talking to anyone in the park until you're ready to do one

This forum is provided by EA but is designed as Player helping Player, in this case we can not do much for you
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