Yu Narukami, the cannon name of the protagonist from Persona 4 and the remake/enhanced version Persona 4: Golden, is constantly pressured by time. He and his band of friends are under a time limit to rescue potential victims of a murderer terrorizing the small town of Inaba, using the strange and dangerous Midnight Channel. Once someone is put inside the TV, Yu and his friends only have until the next rain comes in to get them out before they perish. Yes, it is as strange as it sounds.
With time and weather being so important to the plot, the game is structured around how you choose to spend your time each day marked by days on a calendar. But, as Reddit user CuddlesWithSatan, noticed, Yu's bedroom calendar shows he's a fan of the previous game in the series, Persona 3.
The image is small and hard to make out, but the "P3 Persona 3" text removes any doubt that this calendar is themed on that title. Just like in Persona 4, the calendar is a major component of Persona 3, which has its own Moon Phase System. That makes the calendar a perfect item to represent the previous game in the series, while also being appropriate for Yu to have on his wall.
The only wrinkle in this Easter Egg is that Yu, as well as the main casts of Persona 4, would meet the cast of Persona 3 in the crossover fighting game Persona 4 Arena and Persona 4 Arena Ultimax. Those titles are also canon, which means that Persona 3 shouldn't exist as a game or merchandise in the world of Persona 4. But, on the other hand, perhaps that's looking too deeply into what is otherwise a cool reference to another game in the series implemented well.