It's not possible to transfer an operating system.
What you need to do download Mountain Lion on the MacBook.
Make sure the MacBook meets Mountain Lion requirements > System requirements for OS X Mountain Lion
If it does, on the MacBook, open the App Store then select Purchases from the menu bar.
Locate Mountain Lion then click Install.
Keep in mind, you must use the same Apple ID used for the original purchase of Mountain Lion on the desktop.
To add to Carolyn's advice.
If the Mac you wanted to transfer from came with Mountain Lion, then you cannot transfer or copy it. One, that copy of ML is licensed for the Mac it came on, you cannot share it on your older Macs. Two, it contains hardware drivers only for that Mac, so will not work well, or at all if you try to clone it to your other Mac.