HI,
If you purchased your Mac new it should have come with iMovie pre-installed, without the necessity of you having to manually install it. Try looking in the Applcations folder on your Mac to see if iMovie is there. In the event that you purchased a pre-owned Mac, the previous owner may have deleted iMovie from the Mac. In that case, you would need to use the previous owner's Apple I.D. to obtain an iMovie download. Absent that, you could be out of luck.
In any event, try the following procedure to get an iMovie download. It should work if you ever had iMovie on your Mac before but for some reason it is now missing.
To update/redownload iMovie 10, drag your iMovie 10 app from the Applications folder into the trash, but do not empty the trash. (You can skip that step if you had iMovie 10 on your computer before, but deleted it.) Sign in to the app store and open your purchases folder by clicking on your name at the bottom of the app store side bar. You will see your purchases displayed, including iMovie 10. Redownload/update iMovie from there. If not successful, drag your present iMovie app out of the trash (if you moved it there) and return it to the Applications folder.
If the above procedure does not result in a successful download of iMovie, try contacting Apple Support by clicking on the Get Support item in the upper right hand corner of this forum's screen. Navigate to iMovie by following this path:
Contact Support/See all products and services/Apps and Software/MacApps/iMovie.
Enter you phone number. Perhaps the techs there can give you some guidance.
-- Rich