When rolling a pair of 6-sided dice, each die has 6 faces, resulting in 6 possible outcomes for each die.
To find the total number of possible outcomes when rolling two dice, you can multiply the number of outcomes for the first die by the number of outcomes for the second die:
\[ 6 \text{ (outcomes for the first die)} \times 6 \text{ (outcomes for the second die)} = 36 \]
Therefore, the total number of possible outcomes in the sample space of this experiment is \( \boxed{36} \).