To solve this problem, let's analyze the logic behind the pattern in the given figure.

Observations:

1. Each triangle has three numbers at its vertices.
2. One number is placed at the bottom vertex, which seems to result from a relationship between the two numbers at the top vertices.

Analyzing the first triangle:

• Top vertices: 4, 6
• Bottom vertex: 8

Possible pattern:

If we add the top vertices $4 + 6 = 10$, and subtract $9$ (given in the center of the triangle), we get: $4 + 6 - 9 = 8$

Analyzing the second triangle:

• Top vertices: 2, 4
• Bottom vertex: 6

Using the same pattern: $2 + 4 - 6 = 6$

Applying the logic to the third triangle:

• Top vertices: 5, 7
• Bottom vertex: $?$

Using the pattern: $5 + 7 - 6 = 6$ Thus, the number at the bottom vertex is 6.

Answer:

The missing number is 6, which matches option (C).

Would you like further explanation or have any questions? Below are related questions for practice:

1. What would the bottom number be if the top numbers were $8$ and $3$, and the center number was $4$?
2. How does the logic change if subtraction is replaced with multiplication in a similar triangle problem?
3. Can you derive another possible pattern for these numbers?
4. How would the pattern work if the center number changed dynamically?
5. What happens if we reverse the positions of the top and bottom numbers?

Tip: Always look for addition, subtraction, multiplication, or division relationships when dealing with numerical patterns.