Establish Worker Equivalence

Equate the work done by 12 men to 18 boys to find the efficiency relation: $12M = 18B$.

$12M = 18B \implies 1M = \frac{3}{2}B$

Convert Men to Equivalent Boys

Convert 8 men into equivalent boys using the ratio: $8M = 8 \times \frac{3}{2}B = 12B$.

$8M = 12B$

Calculate Total Combined Workforce

Add the converted men's equivalent to the 6 boys: $12B + 6B = 18B$.

$12B + 6B = 18B$

Determine Completion Time

Since 18 boys take 24 days to complete the task, 18 equivalent boys will also complete it in 24 days.

$24 \text{ days}$