How to create a specific menu for specific users?
This you can do easily with Roles for Menu module.


  This module allows you to restrict access to menu items based on user
  roles. It is used when you don't want to copy your whole menu just
  because for one specific role you want to hide one menu item.



Define the user role (in your case X and Y) in your site.
Then as per user role you can set the menu items, so the menu will be automatically gets display based on Role.


Other similar module is Menu item visibility


  This module exposes configurable and extendable visibility settings
  for menu links.


Both does pretty much similar activity.

Illustration for Menu item visibility module.

Steps:-

1. Module: Download and enable the module.

2. Creating User Role: Now, for example you want to set two user role X and Y. Hence, create by going at People/Permission/Roles -> add two user roles, like userX &amp; userY as shown in following image.


3. Creating a User: Now, create two user, as shown in following image by going at People/ -> add new user, and give corresponding role which we created in step-2. You can see all specifications in the image.


4. Menu item creation: I have created a 7 Menuitems in the section  Main menu by going as Structure/Menus/Main menu.



Now, during the each Menu item creation, you will find the following option at the end of page, and from there selection, FOR WHICH USER YOU WANT TO SHOW THAT MENU-ITEM. Like in follwoing case we want to show Menuitem1 to userX and userY both.



I gave the user role visibility as below, because, I want to show first 4 item to userX Role and all other to userY Role.

Item               Roles Selection 
Menuitem1     userX     userY
Menuitem2     userX     userY
Menuitem3     userX     userY
Menuitem4     userX     userY
Menuitem5               userY
Menuitem6               userY
Menuitem7               userY


5. Test: Now, if you Login using userXexample(which has useX role) you will see only four items, and for userYexample(which has userY role) you will see 7 items.