Let "b" be the number of bicycles and "t" be the number of tricycles, NOT COUNTING Jacky's bike.


Then from the condition, you have this equation


    2b + 3t = 12,      (1)      (counting wheels).


Thus you have one equation for 2 unknowns.
But you have, in addition, a restriction that the solution must be in INTEGER NON-NEGATIVE numbers.


It is very serious restriction, and in your case it provides a unique solution.


With this restriction, equation (1) has these and only these soLutions


    a      b
-------------------

    0       4

    3       2

    6       0


Now, from the condition, it is NATURALLY to assume that  a > 0  and  b > 0.


Then you have ONLY ONE solution  a= 3,  b= 2.


So, there are 3 bicycles and 2 tricycles, not counting Jacky's bike.


In this way, you get the ANSWER :


    there are 3 + 2 = 5 children on the playground, non counting Jacky herself.

    Or 5+1 = 6, counting Jacky.


The problem is solved.