Establish the relationship

Equate the work done by both groups: $6(4M + 4B) = 8(2M + 5B)$.

$24M + 24B = 16M + 40B$

Find the ratio of efficiencies

Rearrange the equation to find the ratio of 1 man ($M$) to 1 boy ($B$): $8M = 16B$, which simplifies to $1M = 2B$.

$\frac{M}{B} = \frac{16}{8} = \frac{2}{1}$

Calculate total work

Substitute $M = 2B$ into the first group's equation to express total work in terms of boys: $6(4(2B) + 4B) = 6(8B + 4B) = 6(12B) = 72B$ units.

$\text{Total Work} = 72 \text{ units of boys}$

Solve for the target group

Convert the target group (12 men + 12 boys) into boys: $12(2B) + 12B = 24B + 12B = 36B$. Time taken = $\frac{72B}{36B} = 2$ days.

$\text{Time} = \frac{72B}{36B} = 2$