Serve these easy pickled veggies alongside sandwiches or hamburgers and hot dogs.
In a large glass jar or bowl, arrange alternating layers of cucumbers and carrots. In a small saucepan, combine sugar, vinegar, the water, salt, mustard seeds, celery seeds, and peppercorns. Bring mixture to a boil over medium-high heat; cook, stirring constantly, just until sugar dissolves.
Remove from heat; pour mixture over vegetables, and let cool completely. Cover tightly, and refrigerate at least 24 hours before serving.
Pickled vegetables can be stored in refrigerator up to 1 week.