This is a combinatorics problem. We can solve it using the multiplication principle. Since the cat has 4 socks and 4 boots, there are 4 ways to choose which sock to put on first. After the first sock is put on, there are 3 socks left to choose from. Once the second sock is put on, there are 2 socks left to choose from. Finally, there is only 1 sock left to put on. Therefore, there are 4 x 3 x 2 x 1 = 24 ways to put on the socks.
After the socks are on, there are 4 boots left to choose from. Once the first boot is chosen, there are 3 boots left to choose from. After the second boot is chosen, there are 2 boots left to choose from. Finally, there is only 1 boot left to choose from. Therefore, there are 4 x 3 x 2 x 1 = 24 ways to put on the boots.
By the multiplication principle, the total number of ways to put on the socks and boots is the product of the number of ways to put on the socks and the number of ways to put on the boots. Therefore, the total number of ways to put on the socks and boots is 24 x 24 = 576.
Therefore, the cat can put on the socks and boots in 576 different ways.
