The main Pokémon games do not let a Pokémon have more than 4 moves at once. A few fan-made battle modes and unofficial formats allow 6 moves, but that is not part of the standard series.

What this means

  • Mainline games: 4 moves per Pokémon.
  • Unofficial/custom formats: can allow 6 moves.
  • Battle balance is one reason the official games keep the 4-move limit.

Where 6 moves appears

  • Pokémon Showdown custom games can use 6-move battling.
  • Forum discussions about “6 moves” are talking about alternative battle formats, not official cartridge gameplay.

Simple answer

If you mean “what Pokémon game has more than 6 moves,” the honest answer is: no official Pokémon game has a Pokémon with more than 4 moves ; only custom or fan formats do.

Information gathered from public forums or data available on the internet and portrayed here.