To solve this expression, we can simplify by combining terms and then isolating x.

Given expression: √(22 + 8√6) - √(22 - 8√6) = 0.12x

First, let's simplify the square roots:

√(22 + 8√6) = √(6 + 16 + 2√6) = √(4 + 6) = √10 = 3.16 (approximately)

√(22 - 8√6) = √(6 + 16 - 2√6) = √(4 + 6) = √10 = 3.16 (approximately)

Now, substitute these values back into the expression:

3.16 - 3.16 = 0

Therefore, the expression simplifies to 0.12x = 0

To isolate x, divide both sides by 0.12:

0.12x = 0
x = 0 / 0.12
x = 0

So, the solution to the expression is x = 0.