In a medium saucepan, begin heating 4 cups of water. Once the water begins to boil, add the 6 tea bags and allow them steep for about 5 minutes. Remove and throw away the tea bags when finished. Set the tea aside to cool.
While the tea is cooling, prepare the simple syrup mixture:
Using a small saucepan, combine one cup of water and one cup of sugar. On medium heat, stir the sugar and water together until the sugar is dissolved and the mixture begins to lightly boil, then remove from heat.
In a large pitcher, combine the tea and the simple syrup. To finish the tea, add in the pureed peaches and the remaining four cups of cool water, stirring all of the ingredients together.
Keep chilled and serve over ice.
Optional: Garnish with peach slices and fresh mint.