The straight-line measurement from one point to another through the origin of a circle is the diameter of the circle.
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Twelve inches is a length. It can be a diameter, but if it is a diameter, you would simply say 'The circle is 12 inches diameter'. So; how big is it - it is 12 inches.
Frisbees come in different sizes. The diameter can be 8 inches, 10 inches, 12 inches, or another diameter.
A circle with a diameter of 12 inches has an area of ~113.1 square inches.
If a circle has a diameter of 12 inches the circumference will be about 37.7 inches. (C = d x Pi)
12 inches because the radius is half of the diameter, and 6 x 2 is 12.