Please Provide Steps For Solving: X+square Root X-4=4?

I interpret your expression of the problem like this ...
x + (√x) - 4 = 4

This sort of problem can usually be solved by isolating the root on one side of the equal sign, then squaring both sides of the equation.
x + (√x) = 8 (add 4 to both sides)
√x = 8-x (subtract x from both sides)
x = (8-x)² = 64 -16x +x²

Now, we can put the equation into standard form and use the quadratic formula.
x² - 17x + 64 = 0 (subtract x from both sides; swap sides)
x = (-(-17) ±√((-17)²-4(1)(64)))/(2*1)
= (17±√(289-256))/2
x = (17±√33)/2
x ≈ {5.6277, 11.3723}

For the solution that is greater than 8, the negative root of the √ must be used.
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Maybe you left out the parentheses.
x + √(x-4) = 4
√(x-4) = 4-x
x-4 = (4-x)2 = 16 -8x +x2
x² -9x +20 = 0
x = (-(-9) ±√((-9)²-4(1)(20)))/(2*1)
x = (9±√(81-80))/2
x = (9±1)/2
x = {4, 5}

The negative square root must be used for x=5.

Check
4 + √(4-4) = 4 (yes)

5 + √(5-4) = 4
5 + √1 = 4
5 -1 = 4 (yes)