Question 657201
THE FIFTH GRADER SOLUTION:
If "each child takes twice the time taken by a man to finish the work", then 2 children do the same work as 1 man, and 6 children would do the work of 3 men.
Then, 6 children and 2 men would do the same work as 3 men and another 2 men, which adds up to 5 men.
The amount of work done was 5 men times 6 days or {{{5*6}}} man-days.
Obviously, 6 men working {{{highlight(5)}}} days will also finish the same {{{5*6}}} man-days job.
 
WHAT THE TEACHER EXPECTS,
I am not exactly sure, because there are many problem-solving recipe books.
I do not know what recipe your teacher uses, but I will try my best guess.
The amount of work done by a person or a group (or some sort of machine, divided by the time worked is the rate of work.
{{{rate=work/time}}}
once we know the rate of work, we can calculate work done over a given period of time, or time required to finish a given amount of work 
If one man would take {{{t}}} days to finish the job by himself, then a child would take {{{2t}}} days.
A man's rate of work would be {{{1(job)/(t(days))=1/t}}}, in jobs per day.
(We could call that the rate of work of a man, {{{r=1/t}}}, in jobs per day, and we would save ourselves from writing so many denominators).
A child's rate of work would be {{{1(job)/(2t(days))=1/2t}}}
The rate of work for a group would be found adding the rates for all the members of the group.
The rate of work for 6 men would be {{{6*(1/t)=6/t}}}.
The rate of work for 2 men and 6 children would be
{{{2*(1/t)+6*(1/2t)=2/t+3/t=5/t}}}
The group of 2 men and 6 children completed 1 job in 6 days, so
{{{6*(5/t)=1}}}job
The group of 6 mean would complete the same job in {{{x}}} days, so
{{{x*(5/t)=6*(5/t)}}}
Multiplying both sides times {{{t}}}, which we know is not zero,
{{{x*(5/t)=6*(5/t)}}} --> {{{5x=6*5}}} --> {{{highlight(x=5)}}} days.