Why the "print" buttons are disabled in my AltiumDesigner project?
The most obvious answer to me would be that you are not focused in the editor window. I notice in your screenshot that you have the "Projects" panel open. If you click on a window, it will "focus" on that panel (You will see the header change color slightly. Usually it is more gray when not focused, and a lighter color when focused). Here is what the top of the Projects panel looks like unfocused and focused:

Non-focused:



Focused:



You can see the color difference in the header bar.

When you're focused in a panel other than the editor, you will not be able to print (you cannot print your "Projects" panel). This is the issue you were having--The print options were grayed out because they are not applicable to the "Projects" panel which you had in focus. When you click on the editor panel, it puts focus on it and the options will be enabled since you CAN print what is in the editor.