A trainer can carry six Pokémon in their active party at one time in the Pokémon TV series.
This six-Pokémon limit is a recurring rule of the Pokémon world and is stated or demonstrated throughout the anime. When a trainer catches an additional Pokémon while already carrying six, the new Pokémon is typically transferred to a professor or another storage system.
The rule helps explain why Ash’s newly caught Pokémon often go to Professor Oak’s laboratory. Ash can continue meeting and catching Pokémon, but only six can normally travel with him as his current party. The laboratory allows his wider collection to remain available for later battles or journeys.
The limit is separate from a battle’s local rules. Some competitions use fewer Pokémon, such as one-on-one or three-on-three matches, but those formats do not change the standard party maximum.