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Explanation:

Step1: Calculate total outcomes

The first - stage has 3 choices (2, 3, 4), and for each choice in the first - stage, the second - stage has 4 choices. By the multiplication principle, the total number of possible outcomes is $3\times4 = 12$.

Step2: Find outcomes with sum greater than 5

List all pairs and their sums:

• If the first number is 2:
  • $(2,4)$ with sum $2 + 4=6$.
• If the first number is 3:
  • $(3,3)$ with sum $3 + 3 = 6$, $(3,4)$ with sum $3+4 = 7$.
• If the first number is 4:
  • $(4,2)$ with sum $4 + 2=6$, $(4,3)$ with sum $4 + 3 = 7$, $(4,4)$ with sum $4 + 4 = 8$. The number of outcomes with sum greater than 5 is 6.

Step3: Find outcomes of spinning the same number twice

The pairs are $(3,3)$ and $(4,4)$. So there are 2 such outcomes.

Answer:

There are a total of 12 possible outcomes. There are 6 possible outcomes for spinning two numbers that have a sum greater than 5. There are 2 possible outcomes for spinning the same number twice.