The control flow diagram for through this method looks like this:

The first linearly independent path through this method is one where the condition for every branch point returns false. The path through the diagram would go Start → count>10 → timesLeft>0 → End. There is also another path where the first condition returns true and hence "The count is large" is printed. This counts as a second independent path because it adds the edges from count>10 → "The count is large" → timesLeft>0 which have not been included in the first path we counted. Likewise the second condition being true would add another independent path through the switch statement and one of its cases. The switch statement has 4 cases that count as paths however one has already been counted in the previous path. As such the switch statement adds another 3 independent paths through the method bringing the total cyclomatic complexity to 6.