Critical Path

B.

The critical path is the longest sequence of tasks that must be completed in order to finish the project on time. In other words, it's the path that determines the project's duration.

To determine the critical path, we need to identify the tasks that have no slack time, meaning any delay in their completion will delay the project's completion.

Given the tasks and their durations, we can create a network diagram to visualize the project's flow and identify the critical path. Here's the diagram:

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Day 1:    Day 2:     Day 3:     Day 4:     Day 5:     Day 6:     Day 7: Task A -> Task A -> Task B -> Task B -> Task C -> Task C -> Task D                                          \________________________/ 

As we can see, Task A starts on Day 1 and takes two days to complete. Task B starts on Day 3 and takes two days to complete. Task C starts after Task A and takes three days to complete. Finally, Task D starts after Task B and Task C and takes one day to complete.

The critical path is the longest path from the start of the project to the end, and it is determined by the tasks that have no slack time. In this case, the critical path is:

Task A (Day 1-2) -> Task C (Day 3-5) -> Task D (Day 6)

Therefore, the duration of the critical path is 6 days.

Answer B, Six days, is the correct answer.