Bring the 8 cups of water to a boil in a tea kettle. Remove the kettle from heat. Place the 4 tea bags in a large pitcher or bowl. Pour the hot water over the tea bags. Let steep for about 5 minutes. Discard the tea bags.
While the tea is still very warm, stir in the honey until it is completely dissolved. Taste for sweetness and add more honey if desired. Set the tea aside to cool to room temperature. You can speed the process by placing it in the refrigerator. Meanwhile, combine the lemon juice and lime juice in a small pitcher.
To make each serving, pour 4 ounces of tea in a glass and add 1 ounce of lemon-lime juice. Add 3 ounces of cold water and ice to fill the glass. Serve with lemon and lime slices.