Facial Excercises Equal Zero Result
Based on the photograph you have submitted, a facial volume enhancer such as Sculptra would be most beneficial. Facial excercises are just about 100% guaranteed to give you no result.
Facial exercises won't affect facial hollowing at all
I wish it was that simple to correct facial hollowing, which is what your photo shows. You would benefit from a filler--I would recommend Sculptra, as it is gradual in onset and the results are long-lasting (at least 2 years, often more, in my personal observation). Sculptra is injected in a simple office procedure with no real downtime (although if you have any bruising, you might consider that downtime). See a plastic surgeon who has injected a LOT of Sculptra, as there is a learning curve associated with the procedure.
Facial Excercises do NOT replace Cheek Volume
All the potential cheek exercising in the world will not replace lost cheek volume. As the amount of caloric use exceeds the intake people lose body and facial fat. Just look at your average decathlon or long-distance runners and see how much fat is present in their faces. The solution to your problem is either an increase in caloric intake or addition of volume (IE fillers) to the area of missing fat (such as fat, Cymetra, Restylane or Juvederm).
Let me add my voice to the chorus of those who feel muscle exercises will not help achieve what you want.
Most of the facial muscles are thin and those which are thicker and stronger might become unattractively more prominent through exercising. The strongest facial muscles are the masseters which helps chewing ( mastication: chewing); the frontalis which lifts your forehead; and the orbicularis oris and ocularis which wrap around the mouth and eyes. Exercising these muscles leads to bulkiness on the sides of the face, forehead lines, crow's feet and smoker's lines respectively. Note: Botox is used in all four areas to relax the muscles and improve physical appearance.
Facial exercises won't help sunken cheeks.
You would be wasting your time. The use of fillers with or without some form of cheeklift or cheek implants is your best bet to do this.
There is no type or intensity of exercise that will lift your facial tissues or restore volume
Unlike the much larger skeletal muscles of the body, there has not been convincing evidence that regular exercise of the facial muscles leads to increase in their volume, or that this would be an aesthetically pleasing improvement.
In fact, the areas in which you (and most people) have lost volume are NOT areas that would be likely to increase in size even if the muscles of your face DID get larger with exercise, as these creases are perpendicular to the muscles themselves...
Your best bet is to pursue fillers for restoration of the lost volume. The result is very pleasing and natural and won't require you to make funny faces in the mirror.
Facial exercises to improve appearance
Facial exercises are unlikely to produce sufficent mass to correct your problem. There are very thin muscles in this area and the facial muscles are composed of fibers that are not likely to bulk up like other muscles such as your pectoralis. They are intended to move against little resistance and respond rapidly.
Facial exercises for fat loss
In my opinion, facial exercises will have little if no effect on your sunken cheeks. You need to replace the lost volume with either fat injections, dermal fillers or cheek implants. I hope this is helpful. Good luck.