Hi Anne,
I have checked the Park Hours for Disney's Hollywood Studios for
August 23, 2016 on the Walt Disney World website and can tell you that
Fantasmic! is currently scheduled to take place at 8:30 PM EST on that particular day whilst
Star Wars: A Galactic Spectacular is currently scheduled to take place at 8:45 PM EST.
With only 15 minutes between the start times for each of these nighttime spectaculars, I'm afraid that it's simply impossible for you to be able to enjoy both on that one day.
If you were to sit towards the back of the theater for Fantasmic! and leave before the masses exit once Fantasmic! has finished, you might be able to catch the end of the fireworks from Star Wars: A Galactic Experience but it would be a rush and I fear that you wouldn't be able to properly enjoy either performance.
Wishing you a magical trip filled with memories which will last a lifetime!
Emma