Find the missing number in the following figure:

In a figure-based number puzzle like this one, the number at the centre of each figure is produced from the four numbers around it by one fixed arithmetic rule. Because two complete figures are shown, that rule can be found by testing simple operations until the same operation produces the exact centre value in both complete figures; the confirmed rule is then applied to the incomplete figure to get the missing number.

1. In the figure whose centre is 17, the four outer numbers are 5, 9, 7 and 4, shown as two connected pairs: 5 with 9, and 7 with 4. Multiplying each connected pair and subtracting one product from the other: (5 x 9) - (7 x 4) = 45 - 28 = 17, which matches the given centre.

2. In the figure whose centre is 27, the four outer numbers are 12, 6, 9 and 5, shown as two connected pairs: 12 with 6, and 9 with 5. Applying the same idea: (12 x 6) - (9 x 5) = 72 - 45 = 27, which again matches. The rule 'multiply each connected pair, then subtract one product from the other' is now confirmed on both complete figures.

3. In the figure with the missing centre, the four outer numbers are 8, 7, 6 and 4, shown as two connected pairs: 8 with 7, and 6 with 4. Applying the confirmed rule: (8 x 7) - (6 x 4) = 56 - 24 = 32.

As an independent check, the plain sum and the plain difference of the four numbers are ruled out as the rule (for the figure whose centre is 17, the sum is 25 and the plain difference is 3, and neither equals 17), and the connected-pair product rule instead matches the centre exactly in both complete figures - so it is applied to the figure with the missing centre with confidence rather than as an untested guess.

So the missing number is 32.