Slice two of the limes and set them aside for garnish. Juice the other 4 limes, you should get about ¾ cup juice, set aside.
Place the mint leaves and granulated sugar in a glass and muddle them well until they are bruised and fragrant, this may take a few minutes. Place the muddled mint into the bottom of your pitcher.
Add the simple syrup, lime juice, and rum to the pitcher. Stir to combine.
Add the club soda and gently stir.
Garnish glasses with lime slices and fresh mint. Add ice to the glasses and pour the mojitos over the ice and serve.
You can use your favorite white rum, I use Bacardi Superior.
Do not skip muddling your mint, it is essential to the flavor of this drink.
To make simple syrup: in a sauce pan put in equal amounts of sugar and water. Stir very well and bring mixture to a gentle boil and continue boiling and stirring until mixture is clear. Allow to cool before using.