After battling picnickers, youngsters, and bug catchers in Route 3, you continue on to Route 4.

Explore Route 4

Near the Route 4 entrance, you can talk to the Coach Trainer to battle Coach Trainer Oberon. He has a level 13 Meowth. You get 1300 Pokédollars for winning. If Meowth used Pay Day, you might get some additional Pokédollars. After the battle, Oberon gives you TM57 Pay Day.

Farther north, you will find a Pokémon Center. In the Pokémon Center, don't buy the Magikarp that the guy tries to sell you. It's not really worth it.

Outside, to the left of the Pokémon Center, there is an Escape Rope.

Go into the tunnel to the right of the Pokémon Center to enter Mt. Moon.