Implementation of drupal behaviours in drupal garden sites If it possible to implement drupal behaviours in drupal garden site? if yes then what will be the syntax for it?
Drupal behaviors are just javascript functions, so the answer is pretty simple:

If the service you're using allows you to add javascript to your pages, then yes, you can use behaviors. If it doesn't, you can't.

Syntax will be identical unless the service uses a patched version of Drupal core. If you have reason to believe they might do, it would be wise to get in touch with them directly and ask.