let 'x' represent the number of gold pieces the first man has and 'y' the number the second man has

give me one third of what you have and three gold pieces more, and I will have three times what you still have

x + ((y/3) + 3) = 3(y - ((y/3) + 3)))

which simplifies to 3x = 5y-36

give me half of yours and two gold pieces more and what you then have will be one ninth of all that I have

x - ((x/2) + 2) = 9(y + ((x/2) + 2)))

which simplifies to -4x = 9y + 20

so we have this system of equations:

3x = 5y-36

-4x = 9y + 20

however, solving this system gives:

x = -9.02

y = 1.78

so this problem makes no sense unless fractional gold pieces are allowed and contains some errors in the problem statement... at best, the problem indicates that the first man is a debtor