I'm a little rusty on this, so this might be wrong.

We know that working rate times time equals the amount of work done, and in the case we can say that finishing an embroidery counts as 1 work done. Also, 3 men working 1 day is that same as 1 man working 3 days.

Let W be the workrate for a woman and M the workrate for a man. Then

the first equation can be written as:

2 for the number of people, and 4 for the hours worked, so the second equation is

Since they both equal 1, they are equal to each other,

Simplifying,

So woman work twice as fast as men. We can plug this into the original equation.

Then we can solve for M

So it takes a woman 18 days to finish the job, and a man 36 days to finish the job.