After playing the game for a few hours, your Grandma will call asking for either Groceries or Fish. Once you hang up, the map above the phone will place a dart on her location.
If she asks for Groceries, she wants milk, sausages, and/or sugar. Taking her any one of these items is enough to pop the achievement.
If she asks for fish, she wants either raw or grilled pike. Raw pike are acquired using the fish trap at the island cottage. Place the trap in the water and give it some time to catch some fish. Raw fish rot quickly, so I recommend using the grill on the island to grill the fish first. You only need one to pop the achievement.
For either option, simply drive to her location with the item(s) she wants, and you'll see a blue basket on a table next to her. Drop the item into that box and the achievement will pop.
Bonus Note: For maxing out the profit of this task, the wiki has a lot of good info and is worth a quick read.
https://my-summer-car.fandom.com/wiki/Bringing_food_to_grand...