Sample space and total possible events Taken from my book:
How many events are there associated with the roll of one die? Solution: Each event corresponds to a subset of {1,2,3,4,5,6}. there are $2^6$ subsets, so there are $2^6$ possible events.
Now my question is: why $2^6$ events? If you roll only one dice shouldn't the possible events be only 6? {1}, {2}, {3}, {4}, {5} and {6}?

You have the terms "event" and "outcome" confused.
The outcomes of the sample space are: $1, 2, 3, 4, 5,$ and $6$.   These are the elements of the sample space:   $\{1, 2, 3, 4, 5,6\}$ .
An event is a set of outcomes.   Such as the event of rolling an even number: $\{2,4,6\}$, the event of rolling a number greater than four: $\{5,6\}$, and such.
There are $2^6$ subsets of the sample space, which are all the plausible events: $\{\}, \{1\}, \{2\}, \{3\}, \{4\}, \{5\}, \{6\}, \{1,2\}, \ldots, \{5,6\}, \{1,2,3\},\ldots,\ldots,\{1,2,3,4,5,6\}$.
The set of these form a sigma-algebra, but that's another topic.
