Distributing 6 cookies can be done in the following ways:
3 chocolate, 3 oatmeal
4 chocolate, 2 oatmeal

Pairing Deborah and Kim (D and K) together, let's examine each way above:

D&K can each have a chocolate cookie, in which case there are 4 choices of children for the remaining chocolate cookie. The remaining children get oatmeal.
4 ways

Same logic holds if D&K get oatmeal cookies instead:
4 ways

Now let's examine the 4 chocolate/2 oatmeal scenario:

D&K get chocolate cookies. Two children can be selected from the remaining 4 to receive the other chocolate cookies as follows;
4!/2!2! = 6 ways. The other 2 children get oatmeal.

D&K get oatmeal cookies. The other children get chocolate. 1 way

Total ways:15,D