1. **State the problem:** Find a number such that doubling the difference of the number and 4 is 6 more than the number. 2. **Define the variable:** Let the number be $x$. 3. **Write the equation:** Doubling the difference of the number and 4 means $2(x - 4)$. The problem states this equals 6 more than the number, so: $$2(x - 4) = x + 6$$ 4. **Solve the equation:** Distribute the 2: $$2x - 8 = x + 6$$ Subtract $x$ from both sides: $$2x - \cancel{x} - 8 = \cancel{x} + 6 \implies x - 8 = 6$$ Add 8 to both sides: $$x - 8 + 8 = 6 + 8 \implies x = 14$$ 5. **Check the solution:** Calculate the left side: $2(14 - 4) = 2(10) = 20$ Calculate the right side: $14 + 6 = 20$ Both sides are equal, so $x=14$ is correct. **Final answer:** The number is $14$.