So was the task 50% complete back in early August or is it 50% complete this week?

If it was 50% complete in early August:

1. Set if 50% complete
2. Tools > Tracking Update Project > Reschedule uncompleted work to start after August 15th.

The task will split with the portion that was 50% complete staying back in early August and the remaining work and duration will be rescheduled to commence on August 15.

If no work was done back in early August, then do step 2 only to reschedule the entire task to begin on August 15th