Mary has $6$ identical basil plants, and three different window sills she can put them on. How many ways are there for Mary to put the plants on the window sills?
Since the plants are indistinguishable, we must only count the number of plants on each window sill.

If all the plants are on one window  sill, there are $3$ ways to choose which window sill they are on.

If $5$ plants are on one window sill and the last is on another, there are $3!=6$ ways to choose which plants go on which window sill.

If $4$ plants are on one window sill and the last two are on another, there are $3!=6$ ways to choose which window sill they are on.

If $4$ plants are on one window sill and the last two are each on one of the other windows, there are $3$ ways to choose which window the $4$ plants are on.

If $3$ plants are on one window and the other $3$ plants are all on another window, there are $3$ ways to choose which window has no plants.

If $3$ plants are on one window, $2$ plants on another window, and $1$ plant on the last window, there are $3!=6$ ways to choose which plants are on which windows.

If $2$ plants are on each window, there is only one way to arrange them.

In total, there are $3+6+6+3+3+6+1=\boxed{28}$ ways to arrange the plants on the window sills.

See if you can find a faster way to do this problem by considering lining up the plants, and placing two dividers among the plants to separate them into three groups corresponding to the sills.