The correct sentence is How many apples are there?.
In sentence construction, A sentence needs to be in line with "Subject + Verb + Object word".
Therefore, looking at the two sentence, The correct sentence is How many apples are there?.
See full question below
When I want to ask how many apples there is in the refrigerator, what is the correct sentence?
1) How many apples are there?
2) How many apples there are?
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