the square root of twice a number is 4 less than the number

Write this out, let the number be x.

sqrt(2x) = x - 4 since 4 less means subtract

Square each side:

sqrt(2x)^2 = (x - 4)^2
2x = x^2 - 8x + 16

Subtract 2x from both sides
x^2 - 10x + 16 = 0

Using the quadratic calculator, we get two potential solutions
x = (2, 8)

Well, 2 does not work, since sqrt(2*2) = 2 which is not 4 less than 2

However, 8 does work:
sqrt(2*8) = sqrt(16) = 4, which is 4 less than the number 8.