Spaying or neutering 68 dogs can prevent a significant number of puppies from being born, considering the reproductive potential of dogs.

Here's a rough estimate:

• A single female dog and her offspring can theoretically produce thousands of puppies over several generations if left unspayed. The average unspayed dog can have 1-2 litters per year, with each litter averaging 4-6 puppies.

• Over the course of 6 years, one unspayed dog and her descendants can produce around 67,000 dogs, though this figure can vary.

Given these numbers, spaying or neutering 68 dogs can potentially prevent tens of thousands, if not hundreds of thousands, of puppies from being born over time. This estimate considers both the direct prevention of litters and the exponential impact of preventing future generations from reproducing.