How could all those animals fit on the Ark?

To answer this question we must first establish what the word, "kind" means in Genesis 6:20 and 7:14. God created a number of different types of animals with much capacity for variation within limits. A larger grouping than what is called a species would, today mostly represent the descendants of each of these different "kinds". In most cases, those species descended from a particular original "kind" and would be grouped today within a classification. An easy way to define what a "species group" is, would be a group of organisms, which can interbreed and produce fertile offspring, yet cannot mate with other species.

I would be comfortable to say that horses, zebras, and donkeys are probably descended from a "horse-like kind", since they can interbreed, although their offspring are sterile. Dogs, wolves, coyotes, and jackals are probably from a "canine kind". Of the 9,000 bird species, approximately 400 are hummingbirds, with only minor differences in color, size, and habitat. Very likely, they too all come from only one or a few "kinds", thereby drastically reducing the total number. The different types of domestic cattle, which are clean animals, are descended from the Aurochs and, as an example; there were probably at most seven, or fourteen, domestic cattle aboard. The Aurochs itself may have been descended from a cattle "kind" including bison's and water buffaloes.

Therefore, many of the variations within a class or group we have today did not exist during the days preceding the flood because they are not original breeds. Many of these modern "kinds" represent horizontal variation (limited adaptation within a group but never with the ability to reproduce outside of that group), and therefore, most creation scientists limit the numbers of different "kinds" to 8000, which includes the extinct "kinds". To be generous, I would say that at the most, about 12,000 individual animals were aboard the ark with a median size of a raccoon while only about 11% would have been much larger than a sheep.

When we analyze just the dinosaurs and their presence on the ark, we must first breakdown and identify just how many dinosaur "kinds" there are. Most secular-paleontologists claim there are 668 dinosaur "kinds" even though many of these "kinds" were named only from a piece of a bone and are probably duplicated many times over thus giving us a greatly exaggerated number. There exists a history of this and we can point to the renaming of the "brontosaur" to the "apadiosaur" as just one example of this. But of those supposed 668, only 106 weighed more than ten tons when fully grown. Moreover, the animals did not need to be full-grown adults nor does the Bible say that. The largest animals were probably represented by "teenage" or even younger specimens, because they weigh less, eat less, and sleep more.

Since marine animals were excluded from the invitation, they died by the billions in the Flood; however, representatives of "each kind" would have survived. As far as the insects, I would speculate that they might not have been on board since they don't breathe air. Insects absorb oxygen through abdominal membranes. They could have survived, particularly in their egg and larvae states, on floating plant debris. Actually, they would be needed worldwide as the Flood ended, to help seeds and sprigs re-germinate and flourish once again.

The Ark itself was enormous! Using conservative measurements, the Ark was about 450 feet by 75 feet by 45 feet, its volume was easily able to house two (or in some cases seven) of each land species, let alone "kinds". The trip may have been difficult for Noah and his family, but it was possible, with God's help.