Young-Earth creationists (YECs) believe that God created the world around 6,000 years ago exactly as described in the book of Genesis. Since creation took place in six 24-hour days (on the 7th day, God rested), they are forced to conclude that dinosaurs were roaming around with Adam and Eve in the Garden of Eden.
They are also forced to conclude, since the world was perfect with no pain, suffering, and death before the Fall, that dinosaurs like T. rex ate coconuts or something with those long, serrated teeth. They also debate whether or not Noah took dinosaurs on the ark (yes, it is surreal, some seriously propose they only took baby dinosaurs since space was at a premium).
By the way, I saw Ken Ham speak once, a long time ago now, when I was a graduate student at the University of Illinois at Urbana-Champaign. Everything he said about geology in that talk (which was given in a church) was a complete lie (I'm not going to be charitable and assume he was just ignorant, because he's not a dumb man - he's a lying sack of shit who lives better than I off the donations of others and outright slanders science and scientists).
Anyhow, here are the pictures I saw posted from his book:
Those large claws on Deinonychus were presumably very useful for pulling branches down so he could eat oranges. And look, Adam has a pet monkey and Eve is feeding a pterosaur (Anurognathus). For an archetypical woman, Eve's a little homely, don't you think?
This next one's just silly.
I guess Ham believes dinosaurs did take a ride on Noah's ark since the text is talking about the time between Noah (Genesis 6) and the Tower of Babel (Genesis 11). Very clever of people at the time to domesticate the dinosaurs and use them as beasts of burden (quite the accomplishment - can you think of any domesticated reptiles today?).
It would be pretty neat to have a tame Gallimimus to saddle up and ride on - like a real live Dinotopia. Unfortunately, since the word "dinosaur" wasn't invented until the 1800s, the ancient Hebrews didn't know what to call them so they got left out of the Bible (maybe the word "camels" is a mistranslation - Jesus may really have said "Again I tell you, it is easier for an Tyrannosaurus to go through the eye of a needle than for someone who is rich to enter the kingdom of God.”
Why not? Makes about as much sense as anything Ken Ham has claimed.