Question 3, A city is building a flower bed in the central square, which is divided into 6 sections (as shown in Figure 1-4). Now, 4 different colors of flowers are to be planted, with one color in each section and no adjacent sections can have the same color, the number of different planting methods is $\qquad$.

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Question 3, A city is building a flower bed in the central square, which is divided into 6 sections (as shown in Figure 1-4). Now, 4 different colors of flowers are to be planted, with one color in each section and no adjacent sections can have the same color, the number of different planting methods is $\qquad$.
Solution: It can be divided into two steps. In the first step, consider planting for $1$, $2$, and $3$, which has a total of $4 \times 3 \times 2=24$ planting methods. In the second step, consider planting for $4$, $5$, and $6$ by classification, and their planting numbers can be calculated by enumeration. When $1$, $2$, and $3$ are planted, assume their colors are (1), (2), and (3); if the color of 4 is (2), then the colors of $5$ and $6$ can be (3), (4) or (4), (3), with 2 planting methods; if the color of 4 is (4), then the colors of $5$ and $6$ can be (2), (4) or (2), (3) or (3), (4), with 3 planting methods. Therefore, when $1$, $2$, and $3$ are planted, $4$, $5$, and $6$ have a total of 5 planting methods.

So the total number of different planting methods is: $2 \times 4 \times 5=120$.