Early release problem - likely to be rejected stating operational difficulties

Hi all, Need some immediate help.
The scenario is I have given my resignation and I have requested for an early release from the company.
However, the manager is saying that is likely to be rejected stating operational difficulties and won't be able to release early.
I have attached the terms which are in my appointment Letter. Pls can some advise what exactly is written?
Does the management hold the power to hold me or does I have the power to buy out the notice period?
I'm ready to pay the 2 month notice period, however the same is mentioned in the appointment letter.
I want to clarify that can the management stop me from buying out the notice period, do they have the authority to reject the buy out options by any means?
Kindly help asap.
14th January 2021 From India, Mumbai

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Have you received your confirmation letter in writing from the company?
While the clause of separation of "appointment is terminable by 2 months notice by either
party or 2 months salary in lieu thereof" is in line with your readiness to buy out notice period,
please peruse the last line of the separation, that is "if the management desires you to continue the employment during notice period, you shall do so".
Your manager might have rejected your plea for early release and quoted "operational difficulties"
based on this stipulation.
So, cooperate with the management, service your 2 months notice period, and have a clean exit.
14th January 2021 From India, Aizawl

Buy out the remaining notice period is not a right to the resigned employee. In deed the privilege lies with the management, it can opt or reject the request of the employee. The organisation has to cope up with the sudden loss of the employee and hence has to be afforded sufficient time to overcome the crisis and train an alternative manpower to the desired level. On your part you can assist the organisation in developing competent man power to replace you.
14th January 2021 From India, Mumbai