General assumptions: Acquiring Silverballers belonging to Agent 47 is the last step that must be done before leaving the gun shop.
If you won shooting range contest, you only have to watch a short cut-scene, during which you'll get back Silverballers.
If you stole a safe keycard then after getting to the main shop room locate a fuse box and sabotage it, doing this when no one looks at your side.
Go to the display case with Silverballers, but do not run to not draw attention on Agent 47. Make sure that there are no guards behind the counter and open the case.
In order to end the mission you have to go to the door shown on the above screen.