36 possible outcomes, assuming replications (ie: rolling a 6 and a 1, rolling a 1 and a 6; counted as two separate outcomes.)
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There are 104, or 10000 permutations of four 10 sided dice.
There is 62 or 36 possible outcomes rolling two dice.
There are 36 possible outcomes: 6 for each die.
For each of the 4 faces on one die, each of the 4 faces on the other die can come up, so there are 4 x 4 = 16 possible outcomes.
You multiply the possibilities so 6 possibilities of the dice and the 10 possibilities of the spinner so in total there are 60 possible outcomes for this situation.