The first paragraph of Genesis seven explains how and why the animals were to be loaded onto the ark. Clean animals came by sevens, and unclean animals in pairs. Both the sevens and the pairs were probably in pairs. So, there were fourteen clean animals and two unclean.
So, just how many is that? We don’t know precisely, but the best guess is about 20,000 to 30,000 animals. I can almost hear the question: “But, aren’t there more species of animals than that? There’s no way millions of species could fit!”
To answer that, I need to explain two things. First, back in Genesis six, God said “And of every living thing of all flesh, you shall bring two of every kind into the ark, to keep them alive with you; they shall be male and female. Of the birds after their kind, and of the animals after their kind, of every creeping thing of the ground after its kind, two of every kind will come to you to keep them alive.” (Genesis 6:19-20, italics in original, bold emphasis mine)
The word kind is much more broad than our word species. There are forty-five species of dolphins in the world1. But, they are very likely only one kind of dolphins. In fact, that kind may include orcas (killer whales), since they can breed with some dolphins2.
So, there are a lot more species than kinds. But, I used the example of dolphins for another purpose as well. Fish and other sea creatures did not board the ark. The ark was for birds and land animals only. So, there might have been 8,000 kinds of animals, some with two representatives and some with fourteen on the ark.