Using the Fundamental Counting Theorem, it is found that there are 648 ways to paint the spinner.
<h3>What is the Fundamental Counting Theorem?</h3>
It is a theorem that states that if there are n things, each with
ways to be done, each thing independent of the other, the number of ways they can be done is:

In this problem, we have that the first sector can be painted in any of the 4 colors, the others until the 5th can be painted in 3 colors(not the adjacent), and the sixth in only 2, as it is adjacent to both the 5th and the 1st sectors, hence:

Hence the number of ways is given by:
N = 4 x 3 x 3 x 3 x 3 x 2 = 648.
More can be learned about the Fundamental Counting Theorem at brainly.com/question/24314866
#SPJ1