Start with task 1 and 2 since they don't have predecessors, as David Espina said. Note when they finish. Now you have task finishing at day 1, task 2 at day 2. (active task #1 at 2; #2 at 2).
Then repeatedly
1. Find the first active task to finish. Here task 1 at day 1.
2. Look at which tasks can now be done. Here that is task 4.
3. Figure when it will finish. That will be day 3.
4. Update the list of tasks. Now you have (#2 at 2, #4 at 3) active.
Then at day 2 task 2 finishes. You can start task 3 and 6. Now you have (#4 at 3, #3 at 5, #6 at 8).
Next task #4 finishes at day 3, but you can't start anything more. That means task #4 isn't on the critical path.
Next task #3 finishes at day 5. You can start task 5 finishing at day 6. Active: (#6 at 8, #5 at 6).
Next task #5 finishes. No new tasks to start. That means task #5 isn't on the critical path. Active #6 at 8)
Next task #6 finishes at day 8.
The last task is on the critical path. Then go backwards. It started when #3 finished, so #3 is on the critical path.
Task #3 started when #2 finished. So #2 is on the critical path.
Task #2 didn't have a predecessor, so it is on the critical path.