For each of 8 colors, I have one shirt and one tie of that color.  How many shirt-and-tie outfits can I make if I refuse to wear a shirt and a tie of the same color?
There are 8 options for the shirt, and only 7 options for the tie because one of the ties has the same color as the shirt, so the number of outfits is $8 \times 7 = \boxed{56}$.