Kanban for scrum team - How the task of story move through the flow

I would like to reupload the photo again.

I also have question(s) related to this board. In case the policy mean when the task in in-progress totally complete, for example we have 3 tasks to implement API and UI. Should we wait until it finish to pull to doing on Test column or we will pull each task finish to test column? which is effective way in these cases?

Is testing really a station at which value is added, or is it another kind of task to be carried out?

Remember that Kanban is a strategy for managing a workflow. The Kanban Guide for Scrum Teams will prove helpful. Things to consider include whether your workflow policies really ought to apply to tasks for example, or to user stories. 

Hi Ian for your question i would say so, it is the flow that define by our team. 

From your suggestion how can we visualize the workflow if task is hidden because we apply policies for story. It means just only story will move through each column, isn’t it?

In Kanban you don't move tasks across the board.  Kanban visualizes the flow of value (i.e. the story) across your workflow (columns).  If you are moving tasks across the board, you are not actually visualizing the value's progress.  

Kanban was originally used by Toyota to help with inventory control.  In that mode, it visualizes the inventory of items flow across the work that used them.  For example brake pads would be the item that traversed the board and each column on the board was a state for the item.  The tasks that were done with the brake pads were not moved across the board.  

Now visualize that concept with software development.  The value is the new feature, upgrade to a component, bug fix, feature enhancement.  Those are what you would want to visualize the progress of by moving it across your board.  Kanban boards can be complex or very simple.  But you want to be able to see where valuable items stall in their progress so complex is not a bad thing.  In your board you have built in 2 queueing points (In-progress/Done, Test/Done).  In Kanban the goal is not to have any queueing states. 

Read the Kanban Guide for Scrum as it has some great information, explanation of how Kanban works and how it can fit within the Scrum framework.

Thank you for very well explanation Daniel, I've already read the Kanban Guide for Scrum team, it still ambiguous for me, so the question came up to my mind when I thought about how the task can go through the process. So after your explanation I think it clear for me now. 

I would also recommend that you review all suggested reading for the PSK as that will broaden your knowledge on the subject too.