Outcomes of the die roll = {1,2,3,4,5,6}
Colors on the spinner = {R, B, Y} (for red, blue, yellow)
There are 6 items in the first set, and 3 items in the second, so 6*3 = 18 items total in the sample space.
Imagine we had a 6 by 3 table.
6 rows and 3 columns
The 6 rows is from the 6 values in {1,2,3,4,5,6}
The 3 columns is from the 3 values in {R, B, Y}
Along the top and left side, list the values mentioned to get this table so far
Now fill in the table by writing the proper letter and number combination. For instance, in row 3, column 2, we will have B3 since "B" is in column 2 and "3" is in row 3. Getting the outcome B3 tells the reader the spinner landed on blue while the die landed on 3. Fill the other 17 cells in a similar fashion and you'll end up with this:
| R | B | Y |
| 1 | R1 | B1 | Y1 |
| 2 | R2 | B2 | Y2 |
| 3 | R3 | B3 | Y3 |
| 4 | R4 | B4 | Y4 |
| 5 | R5 | B5 | Y5 |
| 6 | R6 | B6 | Y6 |
Each of the 18 items inside the table refer to an outcome in the sample space. For instance R2 means the spinner landed on red and the die rolled to a "2".
If you were to erase the table lines and the outer headers, adding in curly braces around the entire thing, then you'd end up with this final sample space
{
R1, B1, Y1,
R2, B2, Y2,
R3, B3, Y3,
R4, B4, Y4,
R5, B5, Y5,
R6, B6, Y6
}
Normally when writing out a set, you write it all as one single line; however, I broke up the set into 6 lines just like how the table is laid out.