Step 1 :Suppose a designer has a palette of 6 colors to work with, and wants to design a flag with 4 vertical stripes, all of different colors.
Step 2 :This is a permutation problem. The designer has 6 options for the first stripe, 5 options for the second stripe (since it can't be the same color as the first), 4 options for the third stripe, and 3 options for the fourth stripe.
Step 3 :So, the total number of possible flags is the product of these options, which is calculated as \(6 \times 5 \times 4 \times 3\).
Step 4 :By calculating the above expression, we get the total number of possible flags as 360.
Step 5 :Final Answer: The total number of possible flags that can be created is \(\boxed{360}\).