There are no equations in this answer, just arithmetic, because that's all that's necessary for a basic estimate using conservation of mass.
How much oxygen do we need?
A resting adult human breathes in and out 7-8 litres of air per minute, which is about 2000 litres in four hours. About 5% of that volume is oxygen that is taken into the bloodstream, recombined as carbon dioxide and exhaled again. So that's 100 litres of oxygen that becomes 100 litres of carbon dioxide. To hold your breath for four hours while resting, you need to be able to:
- Have that much oxygen stored, and release it effectively.
- Be able to scavenge that much carbon dioxide and store it securely.
- When you have access to a breathable atmosphere, dump the carbon dioxide and replenish the oxygen.
- Pay the energy costs of all this extra metabolic work, which will require more oxygen and carbon dioxide storage.
Your time holding your breath will be reduced by exertion, mental stress, and almost anything else other than calm rest, often by quite sizeable factors. If you want to be able to hold your breath for four hours whatever the circumstances, allow a factor of 5.
So you need to be able to store the equivalent of 500 litres of oxygen at atmospheric pressure and temperature. The density of oxygen under those circumstances is 1.429 g/L, so that's about 715g of oxygen. That turns into 985g of carbon dioxide. You need storage for both, and to keep them separate.
This is going to require some major changes to human anatomy and biochemistry.
Managing the job?
To be able to recharge your four hours of breath-holding in four hours in a normal atmosphere, you're going to need to double your rate of gas exchange, by doubling lung volume, which will have obvious effects on the shape of the body.
As for storage, humans use Hemoglobin to transport oxygen. It has a molecular weight of about 64,000, and can store four oxygen molecules, with a total molecular weight of (2*4*16 = 128). So the hemoglobin needed to store oxygen is about 500 times the weight of the oxygen.
Myoglobin can only store one oxygen molecule per myoglobin molecule. It has a molecular weight of about 17,800, and the oxygen molecule has a weight of 32, so the myoglobin has about 560 times the weight of the oxygen, a bit less efficient than haemoglobin.
We need about 358Kg of hemoglobin or somewhat more myoglobin as an oxygen store. That won't fit into a human body, by a long way. There are more compact ways of storing oxygen chemically, but they need much more energy to combine the oxygen, release it, or both.
Conclusion: not practical
This is not possible by genetic engineering if you want the resulting creature to be able to pass for human. You'd probably do better with a cyborg.