The problem states:

A certain number increased by six is equal to twice the same number decreased by four. What is the number?

Let's solve this step-by-step:

1. Let the unknown number be $x$.

2. Translate the statement into an equation: $x + 6 = 2(x - 4)$

3. Expand and simplify the equation: $x + 6 = 2x - 8$

4. Rearrange terms to isolate $x$: $6 + 8 = 2x - x$

   $14 = x$

Thus, the number is $\boxed{14}$.

Would you like further explanation or details on this solution? Let me know!

Related Questions:

1. What happens if the condition changes to “three times the number increased by six”?
2. Can you form and solve a similar equation where the number is halved?
3. How do you verify the solution in such problems?
4. What happens to the equation if subtraction or addition changes?
5. Can you generalize this type of problem to any number?

Tip:

When solving word problems, always translate the text into a clear algebraic equation—it simplifies the process significantly!