1. **State the problem:** Simplify the expression $\frac{2x}{6x}$. 2. **Recall the rule:** When dividing fractions or terms with the same variable, you can divide the coefficients (numbers) and then divide the variables by subtracting their exponents. 3. **Simplify the coefficients:** $\frac{2}{6} = \frac{1}{3}$. 4. **Simplify the variables:** $\frac{x}{x} = 1$ since any nonzero number divided by itself is 1. 5. **Combine the results:** $\frac{2x}{6x} = \frac{1}{3} \times 1 = \frac{1}{3}$. 6. **Final answer:** The simplified form of $\frac{2x}{6x}$ is $\frac{1}{3}$.