"Twice a number" can be written as 2x.
"Two more than twice a number" is 2x + 2.
The problem states that this is equal to the number itself (x). Therefore, we can write the equation:
2x + 2 = x
Subtracting x from both sides gives:
x + 2 = 0
Subtracting 2 from both sides gives:
x = -2
Therefore, the number is $\boxed{-2}$.