To create a tree diagram for rolling a 4-sided die two times, you would start by drawing two branches coming off of a single node. Each branch would represent the possible outcomes of the first roll, which would be 1, 2, 3, or 4. Then, for each of those branches, you would draw four more branches coming off of them, each representing the possible outcomes of the second roll.
The resulting tree diagram would have 16 total branches, each representing a possible outcome of rolling a 4-sided die two times. The sample space would consist of all the possible outcomes of the two rolls, which would be:
(1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (4,4)