Where is Stack Shack Fortnite: How to Catch a Weapon at Stack Shack
Your challenge is to catch a weapon at the Stack Shack, so your first step is to actually get to the Stack Shack. It's located on an island southwest of the Sweat Sands, at the bottom edge of A4. As the water level is still rather high, you can swim (or boat) up and build a short ramp to the house fairly easily.
From here, you just need to grab a fishing rod or harpoon gun and go fishing. There's a barrel of rods right by the house by the chest, and a few spots you can go fishing right from the island.
Getting a weapon by fishing is totally random, so keep at it until you get it. If you don't get a weapon and have exhausted the fishing spots, you will just have to try again later. You just have to catch one weapon to complete the challenge.