This is truly epic.
This is an official liberty request from an Army unit in North Carolina so that a soldier can go visit the Playboy Mansion.
Friends of mine have left the service and visited the mansion (tickets aren't cheap — about $700 for guys), but never have I seen an official request.
The original poster on the Reddit thread where the photo appeared claims he saw his friend post it to Facebook. Personally, I can vouch that this is what a legit liberty request looks like in the military.
As you can see, it was "most definitely" approved:
