This is, of course, pure fiction. But the beauty of the Pokemon HeartGold 4780 meme is how it mimics the old "Mew under the truck" rumors. The number is just random enough to feel cryptic, and just specific enough to make players try it.
Using cheats in Pokémon games usually involves a device like a Gameshark or an emulator with built-in cheat capabilities. The process often includes: pokemon heartgold 4780