is the following rule true?
This not only can be helpful to apply for a refund but also applying for a free ticket.
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The example sentence is incorrect - the two verbs linked by "not only ... but also ..." should be in the same form.
It is also at least a bit awkward because the "can be helpful" is sitting next to one of the verbs. It would be better reworded so that is before the "not only ...":
This can be helpful not only to apply for a refund, but also to apply for a free ticket.
This can be helpful not only for applying for a refund, but also for applying for a free ticket.
Note the extra "for" before "applying" in the second clause - since this came after the "not only", it needs to be repeated after the "but also".