1. **State the problem:** Solve for $x$ in the equation $$6200=12000\left(1-\frac{x}{100}\right)^6.$$\n\n2. **Formula and explanation:** This is an exponential decay type equation where the quantity decreases by a percentage $x$ each period, compounded 6 times. We want to isolate $x$.\n\n3. **Isolate the exponential term:** Divide both sides by 12000:\n$$\frac{6200}{12000} = \left(1-\frac{x}{100}\right)^6.$$\nSimplify the fraction:\n$$0.5167 = \left(1-\frac{x}{100}\right)^6.$$\n\n4. **Take the sixth root:** To undo the power 6, take the sixth root (or raise both sides to the power $\frac{1}{6}$):\n$$\left(0.5167\right)^{\frac{1}{6}} = 1-\frac{x}{100}.$$\nCalculate the left side:\n$$\approx 0.8983 = 1-\frac{x}{100}.$$\n\n5. **Solve for $x$:**\n$$1 - 0.8983 = \frac{x}{100} \implies 0.1017 = \frac{x}{100}.$$\nMultiply both sides by 100:\n$$x = 10.17.$$\n\n6. **Interpretation:** The percentage decrease $x$ is approximately 10.17%.