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If $$x > 2$$ then the number of values of $$x$$ satisfying $$\sqrt{|x - 2|} = \left|\sqrt{x - 2}\right|$$ is
For $$x > 2$$, $$|x - 2| = x - 2$$, so the left side is $$\sqrt{x - 2}$$. The right side is $$\left|\sqrt{x - 2}\right| = \sqrt{x - 2}$$ as well. The equation holds for every $$x > 2$$, so there are infinitely many values.
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