Let S = the number of sons
Let D = the number of daughters

The number of sisters the boy has is the same as the number of daughters.

The number of brothers the boy has is 1 less than the number of sons,
because he is not his own brother.

The number of brothers the girl has is the same as the number of sons.

The number of sisters the girl has is 1 less than the number of daughters,
because she is not her own sister.

So,

NUMBER OF HIS SISTERS = NUMBER OF DAUGHTERS
NUMBER OF HIS BROTHERS = NUMBER OF SONS - 1 
NUMBER OF HER BROTHERS = NUMBER OF SONS
NUMBER OF HER SISTERS = NUMBER OF DAUGHTERS - 1

The first equation comes from:

NUMBER OF HIS SISTERS = NUMBER OF HIS BROTHERS 
  NUMBER OF DAUGHTERS = NUMBER OF SONS - 1
                    D = S - 1

The second equation comes from:

NUMBER OF HER BROTHERS = 2*(NUMBER OF HER SISTERS) 
        NUMBER OF SONS = 2*(NUMBER OF DAUGHTERS - 1)
                     S = 2(D - 1)

       Solve the system of equations:

                     D = S - 1
                     S = 2(D - 1)

Solve that and get D = 3, S = 4.

So their parents have 3 daughters and 4 sons.

Edwin