Let the sphere have radius $ r $. A sphere with radius $ r $ has surface area $ 4\pi r^2 $, so we have \[4\pi r^2 = 196\pi.\] Dividing both sides by $ 4\pi $ yields $ r^2 = 49 $; taking the square root of both sides and keeping the positive solution yields $ r=7 $ inches. A great circle of a sphere is the circular cross-section of the sphere that passes through the sphere's center, which, in this case, is a circle with radius 7. The circumference of this circle is $ 2\pi\cdot 7 = \boxed{14\pi} $ inches.