The Last of Us Part II is filled with safes that you can open to get your hands on some extra loot. They can contain important resources that will help you level skills, and upgrade weapons, so it is well worth the time to find out how to open them all. You can, with some skill, crack the safe, but normally the code will be close by, waiting for you to discover it.
The supermarket in Jackson contains one such safe. As you explore the area, you will come to a part of the building that is filled with spores and will need to put on your gas masks. Go through the crack in the wall, and you will find yourself in a small room. There is one door you can open, and in there you will find the safe. The code for this safe is 7-20-13.
If you want to know how to find the code for yourself or are just curious about what to look out for in similar circumstances in the future, look at the table to the right of the safe. Here you will find a letter saying that a dog has been made employee of the month. Now, head back to the crack in the wall where you entered and look at the bulletin board.
Here, you will find all the employees who won the employee of the month award, including the friendly dog. He won in June 2013. So, 7, 20, and 13. Most of the codes in the game will be hidden similarly and can be discovered by exploring the nearby environment and piecing together some not so obvious clues.