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Kindly, be informed about my leave for the month of October
I would be on vacation with my family starting from 12th Oct to 16th Oct.
Thanks & Regards,
In BrE, we don't use "through" that way. To make it clear that the holiday dates are to include October 16th, we would say "Please note/consider my application for leave from October 12th to October 16th inclusive".
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.