To solve the problem, we use the key property of intersecting rectangles: the product of the areas of opposite regions equals the product of the areas of adjacent regions. This is because the ratios of the heights (or widths) of the overlapping rectangles are consistent.

Step 1: Apply the property

Assuming the given areas are (a = 12), (b = 6), (d = 4), and we need to find (c):
[a \times c = b \times d]

Step 2: Calculate (c)

[12 \times c = 6 \times 4]
[12c = 24]
[c = 2]

Step 3: Sum all areas

[a + b + c + d = 12 + 6 + 2 + 4 = 24]

Answer: (\boxed{24})

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