2. Squeeze out the juice from the limes and the 2 peeled oranges. Reserve.
3. In a medium-size saucepan combine the minced peels, lime juice, orange juice, cranberries, tequila, and sugar. Cover the saucepan with a lid, place over heat, bring to a boil, and let boil rapidly for 8 minutes. Place mixture in mixing bowl and let cool to room temperature.
4. Peel the 4 remaining oranges and separate them into segments. Remove as much membrane and pith as possible. Cut the segments in half. Add segments to the cooled cranberry mixture.
5. Cut the pomegranates in half and remove the seeds with a spoon. Try not to crush the seeds while separating them from the white membrane. Make sure to leave any membrane or white part behind. Using a rubber spatula, combine seeds gently with the cranberry mixture. Chill and serve.
Note: This relish can be made the day before serving.
Harold McGee, the author of Keys to Good Cooking, is an expert on the chemistry behind food and cooking. McGee recently made his first trip to China, where he learned more about rice wine.