﹣Wouldyouliketogoshoppingwithmeafterlunch?﹣I'dloveto,bu...

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﹣Would you like to go shopping with me after lunch?

﹣I'd love to, but I____to go out this afternoon.

A. don't allow B. will allow C. won't be allowed

【解析】句意：-午饭后你愿意和我一起去购物吗？-我愿意去，但是今天下午我不被允许出去。

don’t allow不允许；will allow将会允许；won’t be allowed将不被允许。根据句意可知，主语I和谓语动词allow是被动关系，再根据this afternoon可知，要用一般将来时的被动语态，其构成为will be done，故选：C。