Find a connected graph that has exactly $2$ cutpoints of order $2$ and $3$ cutpoints of order $3$

Question

Find a connected graph that has exactly $2$ cutpoints of order $2$ and $2$ cutpoints of order $3$

Definition: A cut point of order $k$ is a point $a \in X$ whose complement $X-\{a\}$ consists of $k$ path-connected components.

Let the yellow dots be the cutpoints of order $2$ and the red ones of order $3$. How can I connect them to achieve the right graph?

I know that connectedness and path-connectedness are equivalent for graphs.

Answer 1

We need to add some extra vertices: