Thank you very much for answer. My MackBook Air Model is A1466.
Unfortunately, using that model number does not mean much. Apple in their infinite wisdom uses a "model number" scheme that really does not help differentiate between different models. To help illustrate this, this link shows all the "models" that use that model number:http://www.everymac.com/ultimate-mac-lookup/?search_keywords=a1466
That is 9 different "models". Each likely shipped with different macOS versions.
What you will want to provide is the processor specs and the "model year" (i.e. Mid 2012, Mid 2013, Early 2014, or Early 2015). With that, I can tell you (or you can look using that link) what your model came with as the original macOS version.
I can say this, however...which ever version it is, it will support Internet Recovery. The oldest model on that list shipped with 10.7.4 (that would be the Mid 2012 model with the 1.8 GHz i5), so all of them will have Internet Recovery. So, you should be able to hold down the Option-Command-R keys when you reboot the Mac and get to the Internet recovery. This will install either the macOS version that came with the Mac or the closest version that is still available. See footnote #2 for the table in the following link:https://support.apple.com/en-us/HT204904
Acutely i Make a usb Bootable disk(using TransMac but i cant boot using this disk. when Mac starting i tried to press 'option' key but its goes to recovery mode os x utilities.
I can think of three potential reason why it did not boot.
The first would be if the flash drive is not actually getting formatted with a GPT partition. So, you might try the "How to create a GPT partition on a USB flash drive" instructions in the same link in my last post that is AFTER the full TransMac instructions.
The second is that the DMG you have is not of a bootable disk image of the macOS installer and TransMac will only work with a bootable disk image. In other words, it might depend on where/how you got that DMG and what is actually contains. If you extracted it from a El Capitan Upgrade Installer app, then I believe it is not bootable without extra work. And I don't know if TransMac will do that extra work or not.
The last is that the method in the link just does not work. As I said, I have zero experience with TransMac, so I have no clue if that method works or not.
In the end, it should not matter. You can use Internet Recovery to reinstall the macOS. It will be an older version of the macOS, but all the models on the list in the above link can run Sierra. So, whatever version it is, once it is installed and you get the Mac setup with that older macOS version, you can then go into the App Store and "buy" (I put it in quotes because it is a free purchase) Sierra and then upgrade the Mac to Sierra if you want.