We make a chart that lists the possible results for the first spin down the left side, the possible results for the second spin across the top, and the product of the two results in the corresponding cells:
1
2
3
4
1
1
2
3
4
2
2
4
6
8
3
3
6
9
12
4
4
8
12
16
Since each spin is equally likely to stop on 1, 2, 3, or 4, then each of the 16 products shown in the chart is equally likely.
Since the product 4 appears three times in the table and this is more than any of the other numbers, then it is the product that is most likely to occur.