The ratio of parts of vinegar to baking soda for a cleaning mixture is 3 to 1. How many parts of vinegar are needed if there are 6 parts of baking soda?

If the ratio of vinegar to baking soda is 3 to 1, then for every 3 parts of vinegar, there is 1 part of baking soda. Therefore, with 6 parts of baking soda, we would need 6/1 = <<6/1=6>>6 parts of vinegar. Answer: \boxed{6}.