Solution

From the given flowgraph, one longest independent path can be written as:

$1\rightarrow(2,3)\rightarrow6\rightarrow7\rightarrow9\rightarrow10\rightarrow1\rightarrow11$

Now count the nodes in this path:

$1,\ (2,3),\ 6,\ 7,\ 9,\ 10,\ 1,\ 11$

Total nodes $=8$