PowerShell v2+, 49 bytes
(date $args[0].insert(4,'-')-f 'MMMyy').ToUpper()
Takes input $args[0] as an explicit string (e.g., '201604') via command-line input. Uses the string.Insert() function to put a - in the appropriate space, and that resultant string forms input to the Get-Date cmdlet with the -format parameter specifying the three-month shorthand plus two-digit year. We encapsulate that in parens, and tack on a .ToUpper() to make the output string capitalized. That string is left on the pipeline and printing is implicit.