Kangaroos lean back and shake their hands, actually scratching the hair on their chests and stomachs. This is the normal behavior of kangaroo grooming, so you don't have to feel itchy to scratch. Adult kangaroos have the same behavior. Because a kangaroo cub is so cute, it was very popular for a while when it looked up and shook its hand.
As for why they can lean back so steadily, it is inseparable from their tails. Kangaroos' tails are like their "third leg", which is not only used to keep balance, but also to participate in daily walking and running.