What could go in the blank for -(x-8)+4x=+x with infinitely many solutions?

To make the equation into an infinitely many solution, the coefficient and variable on each side must be the same. Let's see how it goes.
-(x - 8) + 4x = 2(__) + x
-x + 8 + 4x = 2(__) + x
3x + 8 = 2(__) + x
3x - x + 8 = 2(__)
2x + 8 = 2(__)
(2x+ 8)/2 = (__)
x + 4 = (__)

Therefore, the answer of the blank will be x + 4.

Let's verify.
-(x - 8) + 4x = 2(x + 4) + x
-x - 8 + 4x = 2x + 8 + x
3x + 8 = 3x + 8
As you can see each side has the same coefficient and variable which is 3x. Once you subtract them, you will get zero. You can't solve for x as well.