Dishonored Guide: Opening the Art Dealer’s Safe (Distillery District in House of Pleasure Quest)
The number combination is 138. This guide explains how to open the safe without that knowledge.
You aren’t supposed to be able to open the safe until you have spoken to the art dealer and you only do that in the House of Pleasure quest. I’m also not sure if you will even be able to open it until you have spoken to him, be sure to leave a comment below if you have tried before speaking to the art dealer.
There is a visual version of this guide at the end of this guide.
When you speak to the art dealer just keep electrocuting him until a conversation option pops up where you ask for the combination.
You can open the safe and loot it and still turn in the optional quest to Slackjaw and get your non-lethal elimination.