Hi Nazima,
Sorry to hear you having issues with Honda Turkey, it can be extremely frustrating when paying for such an expensive car , and then when something goes wrong the dealer and Honda refuse to assist to fix the issue.
I'm no Expert in Turkey law, but just a few questions to help clarify the issue and help you move forward on your issue
1) Confirm if your car still has a manufacturer warranty, sometimes if you buy a car second hand the previous owner could have voided your warranty.
2)Contact Honda and request a copy of the Vehicle warranty. Read over your warranty and confirm that you yourself as a owner are not in breach of any of the terms and conditions of your warranty agreement.
3)once you are 100% certain that your warranty is still active, write a letter to Honda Turkey and request them to supply a reason that they do not wish to fulfil your repairs.
4) And this is where it gets to the hard part, depending on the laws of your country and the legal mechanisms in place, Most consumer protection laws require the owner of the car to prove that the current issue was not caused as a result driver error/abuse. This can be very difficult given the only why to prove this would be to open the gearbox and inspect the route cause of the issue , thereby removing the warranty
This can also be an expensive task and also very time consuming, once you have this proof you would then need a lawyer to take action against Honda. This is very long process and generally leads to you spending more money than the original quote of 3000$ to fix the gearbox
This is why many countries have a "consumer protection act" in place so that disgruntled consumers like yourself who are being pushed around, can use these systems to report and take effective action to protect your rights.
In the UK they have the "themotorombudsman.org" And in South Africa we have "miosa.co.za" that can help us enforce our legal rights.
I would advise doing some research on the details of your local law and how it applies to your situation and if you have the equivalent to the above organisations to help assist you with solving your issue.
With the right knowledge the Law can be used in your favour.
Otherwise if your warranty is void , take your car down to your local tuner and ask for some advise and prices to get it repaired, they will probably do a better job anyway and for cheaper
Sorry I cant be of much help as I truthfully feel your frustrations