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How many rabbits did he have left? How many of the six pennies did she have left? How many boats did Joe have left?

Are the above sentences acceptable? If you are a teacher of English, will you advise your students to avoid such usage?
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How many rabbits did he have left? How many of the six pennies did she have left? How many boats did Joe have left?
Are the above sentences acceptable? Yes. Perfect.

If you are a teacher of English, will you advise your students to avoid such usage? No. There is no need to avoid this usage.

How many ... s did X have left? = How many ...s remained in X's possession?

CJ
Comments  
They’re all fine. The examples in your title have different meanings:

How many marbles did he have left? = how many did he keep after some were taken away from him?

How many marbles did he leave? = how many did he put down and walk away from?

Lil' Ruby Rose
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Teo,

Although your example sentences sounded a little odd, the structure is correct.

How many hours do we have left before the deadline?

Deadline is tomorrow and we only have a few hours left to finish the project.

How much money do you have left in your wallet?

implies that still remains. If we started with certain amount of time or quantity of something, and you wanted to know how much still remains, you can use in that context.
 CalifJim's reply was promoted to an answer.