And... if you just want a written out solution...
Suppose the six cookies to be chosen are the stars, as we attempt to implement stars and bars.
We take two dividers, and place them between the cookies, such that the six cookies are split into 3 groups, where the groups are the number of chocolate chip, oatmeal, and peanut butter cookies, and each group can have 0.
First, assume that the two dividers cannot go in between the same two cookies.
By stars and bars, there are \(\binom{7}{2}\) ways to make the groups.
Finally, since the two dividers can be together, we must add those cases where the two dividers are in the same space between cookies. There are 7 spaces, and hence 7 cases.
Our final answer is\(21 + 7 = \boxed{28}\) assortments.