1. Calculate the area of the 6-inch pizza using A_{6} = \pi (3)^2 = 9\pi.
2. Calculate the area of the 12-inch pizza using A_{12} = \pi (6)^2 = 36\pi.
3. Determine that the 12-inch pizza's area is 4 times that of the 6-inch pizza: \frac{A_{12}}{A_{6}} = 4 .
4. Calculate the total calories for the 12-inch pizza (2400) by multiplying the 6-inch pizza's calories (600) by 4.
5. Divide the total calories of the 12-inch pizza (2400) by the number of slices (8) to find that each slice contains 300 calories.
6. The answer is that one slice of the 12-inch pizza contains 300 calories.