Help Moving Object

I would like to know how can i move this object at local axis , cuz everytime i try it doesn’t work

The local axis is the local axis of the OBJECT, if you have rotated the mesh in edit mode this may not be the same as the direction the MESH is pointing. We cannot tell as we don’t have access to your blend file

You can set a custom orientation

i imported the object like that from fbx

Thanks that custom feature of blender is quite useful and easy to apply , btw is there a way to make object linked for example if i edit one window , all of them will change , i tryed Ctrl-l and object data but they disappear and only the active one remains
Happy new year btw xD