In a medium saucepan, bring the rice and 2 cups water to a boil; lower the heat, cover and simmer until the water is absorbed, about 20 minutes. Let stand, covered, for 5 minutes.
Meanwhile, in a large nonstick skillet, heat 3 tablespoons olive oil over medium-high heat. Add the shrimp and cook for 2 minutes. Stir in the sugar snap peas, season with salt and pepper and cook until the shrimp is opaque, about 1 minute. Transfer to a large bowl.
Place the skillet over medium-high heat and add the remaining 3 tablespoons olive oil, the scallion whites and garlic. Cook, stirring, until the garlic sizzles, about 30 seconds. Stir in the rice, season with salt and pepper and spread into an even layer. Cook until slightly browned, 3 to 4 minutes. Stir and cook for 3 minutes more. Push the rice to one side of the pan; add the eggs, season with salt and cook, scrambling, until set, 1 to 2 minutes. Stir the eggs into the rice, then add the shrimp mixture, peas and carrots and scallion greens and cook, stirring, until heated through.