The problem involves three figures with four numbers surrounding a central number. We need to find the pattern used in the first two figures to determine the missing number in the third figure.

Let’s analyze the first two figures:

1. First figure:
   Numbers surrounding the center: 2, 6, 6, 8
   Central number: 36
   Calculation:
   $(2 \times 6) + (6 \times 8) = 12 + 48 = 60$
   But the central number is 36, so there is likely a subtraction rule involved.
   Pattern:
   $60 - 24 = 36$, where 24 could be a constant or related to the numbers.

2. Second figure:
   Numbers surrounding the center: 2, 5, 8, 7
   Central number: 46
   Calculation:
   $(2 \times 5) + (8 \times 7) = 10 + 56 = 66$
   Again, the central number is less than this result.
   Pattern:
   $66 - 20 = 46$, where 20 could be a similar adjustment factor.

Now let’s apply this to the third figure:

3. Third figure:
   Numbers surrounding the center: 4, 5, 6, 10
   Missing central number: ?
   Calculation:
   $(4 \times 5) + (6 \times 10) = 20 + 60 = 80$
   Using a similar pattern of subtraction, we can hypothesize that 80 minus a constant (in line with the previous figures) will give the central number.
   Since the subtraction values seem to follow a slight progression (24, 20), the missing number could be found by subtracting 18:
   $80 - 18 = 62$.

Thus, the missing number is 62.

Would you like further details or have any questions? Here are five related questions:

1. What other patterns could be used to solve problems like this?
2. How would the pattern change if subtraction wasn't involved?
3. What role do the surrounding numbers play in the relationship with the central number?
4. How could you use algebra to generalize this type of problem?
5. Are there other mathematical operations besides addition and multiplication that could work in these puzzles?

Tip: Always check for both addition and subtraction patterns when working with number placement puzzles.