There is 1 more post than there are sections of fence between the posts.

He was originally planning to have N posts and N-1 2m sections of fence
between the posts, like this:

|  2m  |  2m  |  2m  |  2m  |  2m  |  ....  |  2m  |

But short of money he decided to have N-3 posts and N-4 3m sections of
fence between the posts instead, like this:

|   3m   |   3m   |   3m   |   3m   | ... |   3m   |


So  (N-1)×2 = (N-4)×3

    
     2(N-1) = 3(N-4)
     2N - 2 = 3N - 12
         -N = -10
          N = 10

So he was going to have 10 posts and 9 2m sections of fence between
them, so his property is 9×2m = 18m wide.

To check:  Instead he used 7 posts and 6 3m sections of fence between
them, so his property is 6×3m = 18m wide.  

So both ways his property is 18m wide.

Edwin