[c22]

I dunno, I immediately noted that 12 hens must lay 12 eggs in 3 days (it takes 3 days for a hen to lay an egg). Then I just asked myself how many 3-days are in 12-days--okay, 12 [eggs] * 4 [3-day egg periods] = 48...

I didn't need to resort to pen and paper, but I'm also not in primary school.

[jimmaswell]

I always skip straight to dimensional analysis for such a thing.

3 eggs / 3 chickens / 3 days * 12 chickens * 12 days cancels out to 48 eggs

[jkubicek]

There are a lot of right ways to solve this problem, but this is clearly the most fun way.